# How do you find the square root of a number that is not a perfect square without a calculator?

## How do you find the square root of a number that is not a perfect square without a calculator?

Finding square roots of of numbers that aren’t perfect squares without a calculator

1. Estimate – first, get as close as you can by finding two perfect square roots your number is between.
2. Divide – divide your number by one of those square roots.
3. Average – take the average of the result of step 2 and the root.

### What happens when you take the square root of a non perfect square number?

The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can’t be written as the quotient of two integers. The decimal form of an irrational number will neither terminate nor repeat.

How do you find the number of non perfect squares?

The square of a number is that number times itself. Here are the square roots of all the perfect squares from 1 to 100. A non-perfect square is every number that is not the result of squaring an integer with itself. 2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26 etc…

How do you find the square root of a non perfect number by division?

Division Method

1. Take the number whose square root is to find.
2. Place a bar over every pair of the digit of the number starting from that in unit’s place (rightmost side).
3. We divide the leftmost number by the largest number whose square is less than or equal to the number under the leftmost bar.

## How do you find the square root of an odd number?

Mrs Brooksbank (a maths teacher) told us to subtract the odd numbers in order 1,3,5,7 etc. until you get to zero then count up the number of subtractions! Total number of subtractions = 6 therefore the square root of 36 = 6.

### What is an example of a non perfect square?

Please note that all the perfect square numbers end with 0, 1, 4, 5, 6 or 9 but all the numbers with end with 0, 1, 4, 5, 6 or 9 are not perfect square numbers. Example, 11, 21, 51, 79, 76 etc. are the numbers which are not perfect square numbers.

How do you find a non perfect square between two square numbers?

(n+1)2−n2=(n2+2n+1)−n2=2n+1. So, we find that between n2and(n+1)2 there are 2n numbers which is 1 less than the difference of two squares. Therefore, non perfect square numbers between 21 and 22= 2n= 2× 21 = 42. So, the non-perfect square number between 21 and 22 is 42.

Why is 7 not a perfect square?

7 is not a perfect square because you cannot express it as the product of two equal integers.

## What are imperfect square roots?

Imperfect squares are numbers whose square roots contain fractions or decimals. For example: √20 ≈ 4 ½ √77 ≈ 8.77. If a whole number is not a perfect square, than the square root is an irrational number.

### Which of these is a non-perfect square number?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 and 400. and you will find that all of them are ending with 0, 1, 4, 5, 6 or 9. So it means that all the non-perfect square numbers end with 2, 3, 7 or 8.

What is a non-perfect square root called?

If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating).