Name: Estimation of Square Roots
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: For not-perfect squares, we can estimate their square root to the closest whole number. Learn how to estimate the square root of non-perfect squares.

Question

Observe the following pattern and fill in the blanks:

$5^{2} = 0 \times 100 + 5^{2} = 25 15^{2} = 1 \times 200 + 5^{2} = 225 25^{2} = 2 \times 300 + 5^{2} = 625$

$35^{2} =$ _____ $= 1225$

$45^{2} = 4 \times 500 + 5^{2} =$ _____

_____ $^{2} = 5 \times 600 + 5^{2} =$ _____

$65^{2} =$ _____ $=$ _____

Accepted Answer

Observe the following pattern and fill in the blanks:

$5^{2} = 0 \times 100 + 5^{2} = 25 15^{2} = 1 \times 200 + 5^{2} = 225 25^{2} = 2 \times 300 + 5^{2} = 625$

$35^{2} =$ _____ $= 1225$

$45^{2} = 4 \times 500 + 5^{2} =$ _____

_____ $^{2} = 5 \times 600 + 5^{2} =$ _____

$65^{2} =$ _____ $=$ _____

In $15^{2}$ we can see the digit at tens place is multiplied with hundred of the number next to the digit present at tens place and then add square of $5$ .

$35^{2} = 3 \times 400 + 5^{2} = 1200 + 25 = 1225$

$45^{2} = 4 \times 500 + 5^{2} = 2000 + 25 = 2025$

$55^{2} = 5 \times 600 + 5^{2} = 3000 + 25 = 3025$

$65^{2} = 6 \times 700 + 5^{2} = 4200 + 25 = 4225$

Hence, the required answer is

$5^{2} = 0 \times 100 + 5^{2} = 25 15^{2} = 1 \times 200 + 5^{2} = 225 25^{2} = 2 \times 300 + 5^{2} = 625$

$35^{2} = 3 \times 400 + 5^{2} = 1225$

$45^{2} = 4 \times 500 + 5^{2} = 2025$

$55^{2} = 5 \times 600 + 5^{2} = 3025$

$65^{2} = 6 \times 700 + 5^{2} = 4200 + 25 = 4225$

Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Squares and Square Roots, Exercise 3: Exercise 2.2

Rupesh Pathak Mathematics Solutions for Exercise - Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Squares and Square Roots, Exercise 3: Exercise 2.2

Questions from Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Squares and Square Roots, Exercise 3: Exercise 2.2 with Hints & Solutions

Learn and Prepare for any exam you want !