### Chapter 3 Squares and Square Roots – Exercise 3.7 | Set 1

**Question 11) 9998.0001**

**Solution:**

Hence, the square root of 9998.0001 is 99.99.

**Question 12) 0.00038809**

**Solution:**

Hence, the square root of 84.8241 is 9.21.

**Question 13) What is that fraction which when multiplied by itself gives 227.798629?**

**Solution:**

We have to find the square root of the given number :

Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093.

**Question 14) The area of square playground is 256.6404 square meters. Find the length of one side of the playground.**

**Solution:**

The length of one side of the playground is the square root of its area

So, the length of one side of the playground is 16.02 meters.

**Question 15) What is the fraction which when multiplied by itself gives 0.00053361?**

**Solution:**

We have to find the square root of the given number :

Hence, the fraction, which when multiplied by itself, gives 0.00053361 is 0.0231.

**Question 16) Simplify:**

**Solution:**

**1)** First, finding the square roots of 5.29 and 59.29

On putting the values on their respective positions, we have (7.7 – 2.3) / (7.7 + 2.3) = 5.4/10 = 0.54.

Hence, the answer is 0.54.

**2)** First, finding the square roots of 0.2304 and 0.1764

On putting the values on their respective positions, we have (0.44 + 0.42) / (0.44 – 0.42) = 0.9/0.06 = 15.

Hence, the answer is 15.

**Question 17) Evaluate √50625 and hence find the value of √506.25 + √5.0625**

**Solution:**

Next, we calculate √506.25 and √5.0625

√506.25 = (√50625)/(√100) = 225/10 = 22.5

√5.0625 = (√50625)(√10000) = 225/100 = 2.25

√506.25 + √5.0625 = 22.5 + 2.25 = 24.75.

**Question 18) Find the value of √103.0225 and hence find the value of:**

1) √10302.25 2) √1.030225

**Solution:**

First, finding the square root of 103.0225

Hence, the square root of 103.0225 is 10.15

Now, we can solve the following questions as shown below:

1)√10302.25 = (√103.0225)×(√100) = 10.15×10 = 101.5

2)√1.030225 = (√103.0225)/(√100) = 10.15/10 = 1.015

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