In square root of number in the fraction form, suppose the square root of a fraction **\(\frac{x}{a}\)** is that fraction **\(\frac{y}{a}\)** which when multiplied by itself gives the fraction **\(\frac{x}{a}\)**.

If x and y are squares of some numbers then,

If the fraction is expressed in a mixed form, convert it into improper fraction.

Find the square root of numerator and denominator separately and write the answer in the fraction form.

**1. Find the square root of \(\frac{625}{256}\)**

Solution:

\(\sqrt{\frac{625}{256}} = \frac{\sqrt{625}}{\sqrt{256}}\)

Now, we find the square roots of 625 and 256 separately.

Thus, √625 = 25 and √256 = 16

⇒ \(\sqrt{\frac{625}{256}} = \frac{\sqrt{625}}{\sqrt{256}}\) = \(\frac{25}{26}\)

**2. Evaluate: \(\sqrt{\frac{441}{961}}\).**

Solution:

\(\sqrt{\frac{441}{961}} = \frac{\sqrt{441}}{\sqrt{961}}\)

Now, we find the square roots of 441 and 961 separately.

Thus, √441 = 21 and √961 = 31

⇒ \(\sqrt{\frac{441}{961}}\) = \(\frac{\sqrt{441}}{\sqrt{961}}\) = \(\frac{21}{31}\)

**3. Find the values of \(\sqrt{\frac{7}{2}}\) up to 3 decimal places. **

Solution:

To make the denominator a perfect square, multiply the numerator and denominator by √2.

Therefore, \(\frac{\sqrt{7} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}\) = \(\frac{\sqrt{14}}{2}\)

Now, we find the square roots of 14 up to 3 places of decimal.

Thus, √14 = 3.741 up to 3 places of decimal.

= 3.74 correct up to 2 places of decimal.

Therefore, \(\frac{\sqrt{14}}{2}\) = \(\frac{3.74}{2}\) = 1.87.

**4. Find the square root of 1\(\frac{56}{169}\)**

**Solution: **

1\(\frac{56}{169}\) = \(\frac{225}{169}\)

Therefore, \(\sqrt{1\frac{56}{169}}\) = \(\sqrt{\frac{225}{169}} = \frac{\sqrt{225}}{\sqrt{169}}\)

We find the square roots of 225 and 169 separately

Therefore, √225 = 15 and √169 = 13

⇒ \(\sqrt{1\frac{56}{169}}\) = \(\sqrt{\frac{225}{169}} = \frac{\sqrt{225}}{\sqrt{169}}\) = \(\frac{15}{13}\) = 1\(\frac{2}{13}\)

**5. Find the value of \(\frac{\sqrt{243}}{\sqrt{363}}\).**

**Solution: **

\(\frac{\sqrt{243}}{\sqrt{363}}\) = \(\sqrt{\frac{243}{363}}\) = \(\sqrt{\frac{81}{121}} = \frac{\sqrt{81}}{\sqrt{121}}\) = \(\frac{9}{11}\)

**6. Find out the value of √45 × √20.**

Solution:

√45 × √20 = √(45 × 20)

= √(3 × 3 × 5 × 2 × 2 × 5)

= √(__3 × 3__ × __2 × 2__ × __5 × 5 __)

= (3 × 2 × 5)

= 30.

● **Square Root**

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**Square Root of a Perfect Square by Using the Long Division Method**

**Square Root of Numbers in the Decimal Form**

**Square Root of Number in the Fraction Form**

**Square Root of Numbers that are Not Perfect Squares**

**Practice Test on Square and Square Roots**

● **Square Root- Worksheets**

**Worksheet on Square Root using Prime Factorization Method**

**Worksheet on Square Root using Long Division Method**

**Worksheet on Square Root of Numbers in Decimal and Fraction Form**

**8th Grade Math Practice** **From Square Root of Number in the Fraction Form to HOME PAGE**

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