Square Root of Numbers that are Not Perfect Squares

Square root of numbers that are not perfect squares or to find the value of square root correct up to certain places of decimal are:



If we have to find the square root of a number up to ‘n’ places of decimals, the number of digits in the decimal part must be 2n. If they are less than 2n, then affix suitable number of zeros to the extreme right of the decimal part.

Find the square root of decimal number using long division method.

But if we have to find the square root of number correct up to ‘n’ places of decimal, then find the square root of number up to (n + 1) places of decimal.

If the digit at the (n + 1) decimal place is equal to 5 or greater than 5, then the digit at ‘n’ place increases by 1.

If the digit at (n + 1) decimal place is less than 5, then the digit at ‘n’ place remains the same and deletes the digit at (n + 1) place.

This is how we find the square root correct up to n decimal places.

Examples on square root of numbers that are not perfect squares are given below;

1. Evaluate √2 correct up to two places of decimal.

Solution:

Using the division method, we may find the value of √2;

Therefore, √2 = 1.414     ⇒     √2 = 1.41 (correct tip to 2 places of decimal)


2. Evaluate √3 correct up to 3 places of decimal.

Solution:

Using the division method, we may find the value of √3;

Therefore, √3 = 1.7324     ⇒     √3 = 1.732 (correct tip to 3 places of decimal)

3. Evaluate √0.8 correct up to two places of decimal.

Solution:

Using the division method, we may find the value of √0.8 as shown below.

Therefore, √0.08 = 0.894     ⇒     √0.8 = 0.89 (correct tip to 2 places of decimal)



Square Root

Square Root

Square Root of a Perfect Square by using the Prime
   Factorization Method

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

Table of Square Roots

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

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