Arrange the following in the descending order 23 - 21 ) , ( 19 - 17 ) , ( 21 - 19 .

19 - 17 ) > ( 21 - 19 ) > ( 23 - 21

23 - 21 ) > ( 21 - 19 ) > ( 19 - 17

23 - 21 ) > ( 19 - 17 ) > ( 21 - 19

21 - 19 ) > ( 23 - 21 ) > ( 19 - 17

Find the square root of 1625

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Consider the following numbers:

$1 . 2222 2 . 11664 3 . 343343 4 . 220347$

Which of the above are not perfect squares?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

How many numbers are there between

200

to

300

which are perfect cubes?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Find the square root of $6889$ by using Dwandwa Yoga Method.

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

What is the natural number n for which 39 +312 +315 + 3n is a perfect cube of an integer ?

HARD

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The LCM of two numbers is

168

and their HCF is

12

. If the difference between the numbers is

60

. What is the sum of the numbers?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

What is the square root of

23 - 4 \sqrt{15}

?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The cube root of

3375

equal to_____.

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Which is the smallest perfect square number exactly divisible by

4, 5, 6

and

9

?

MEDIUM

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The square root which of the following is a rational number?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

\sqrt[3]{a} = \sqrt[3]{9} + \sqrt[3]{126} + \sqrt[3]{217}

, then which of the following is correct?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

What is the value of

2 + \sqrt{2 + \sqrt{2 + \sqrt{. . . . . . . . . .}}}

?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Arrange the following in the descending order $(\sqrt{23} - \sqrt{21}), (\sqrt{19} - \sqrt{17}), (\sqrt{21} - \sqrt{19})$ .

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

What is the least number that should be added to the product of

7 \times 8 \times 9 \times 10

to make it a perfect square?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

What is the value of

\sqrt[3]{4 \frac{12}{125}}

?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The smallest integer with

4

digits which is a perfect square is:

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

\frac{\sqrt{50} + \sqrt{98}}{\sqrt{18}} = ?

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The value of

\sqrt{10 + \sqrt{24 + \sqrt{131 + \sqrt{153 + \sqrt{256}}}}}

is

MEDIUM

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Which of the following is a perfect cube.

MEDIUM

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The students of a class donated a sum of

₹ 2, 809

to a fund. Each student donated as many rupees as the number of students in the class. The number of students in the class is:

EASY

Mathematics>Algebra>Expressions and Equations>Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

The value of

\sqrt{40 + \sqrt{9 \sqrt{81}}}

is:

Find the square root of $\frac{16}{25}$

Important Questions on Expressions and Equations

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