Monica Capoor Solutions for Chapter: Squares and Square Roots, Exercise 3: EXERCISE

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of ${136}^2-{135}^2$ 

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of ${98}^2-{97}^2$ 

Observe the following pattern.

$$\begin{gathered} 2^2-1^2=2+1; \\ {3}^2-2^2=3+2; \\ {4}^2-3^2=4+3; \\ {5}^2-4^2=5+4 \end{gathered}$$

Now, find the value of the ${121}^2-{120}^2$ .

Observe the following pattern and fill in the missing numbers.

$$\begin{gathered} 1^2=1 \\ {2}^2=1+3 \\ {3}^2=1+3+5 \\ {4}^2=1+3+5+7 \\ {5}^2=1+3+5+7+9 \\ ⋮ \\ {9}^2=1+3+5+7+9+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_+\_\_\_\_\_ \\ ⋮ \\ \_\_\_\_\_=1+3+5+7+9+11+13+15+17+19+21 \end{gathered}$$

Find the square of $65$ considering that it has $5$ in the units place.

Find the square of $75$ considering that it has $5$ in the units place.

Evaluate using the identity $(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})={\mathrm{a}}^2-{\mathrm{b}}^2$.

$49\times 51$

Evaluate using the identity $(\mathrm{a}+\mathrm{b})(\mathrm{a}-\mathrm{b})={\mathrm{a}}^2-{\mathrm{b}}^2$.

$68\times 72$