Architecture

# How To Find The Square Root Of 40 In Radical Form, Simplify Square Root Of 40

As you should know from your high school algebra course, the square root y of a number x is such that y2 = x. By multiplying the value y by itself, we get the value x. For instance, 6.3246 the square root of 40 because 6.32462 = 6.3246×6.3246 = 40.

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Square root of 40 = 6.3246

## Is 40 a Perfect Square Root?

No. The square root of 40 is not an integer, hence √40 isn”t a perfect square.

Previous perfect square root is: 36

Next perfect square root is: 49

## How Do You Simplify the Square Root of 40 in Radical Form?

The main point of simplification (to the simplest radical form of 40) is as follows: getting the number 40 inside the radical sign √ as low as possible.

40= 2 × 2 × 2 × 5= 210

## Is the Square Root of 40 Rational or Irrational?

Since 40 isn”t a perfect square (it”s square root will have an infinite number of decimals), it is an irrational number.

## The Babylonian (or Heron’s) Method (Step-By-Step)

StepSequencing
1

In step 1, we need to make our first guess about the value of the square root of 40. To do this, divide the number 40 by 2.

As a result of dividing 40/2, we get the first guess: 20

2

Next, we need to divide 40 by the result of the previous step (20).40/20 = 2

Calculate the arithmetic mean of this value (2) and the result of step 1 (20).(20 + 2)/2 = 11 (new guess)

Calculate the error by subtracting the previous value from the new guess.|11 – 20| = 99 > 0.001

Repeat this step again as the margin of error is greater than than 0.001

3

Next, we need to divide 40 by the result of the previous step (11).40/11 = 3.6364

Calculate the arithmetic mean of this value (3.6364) and the result of step 2 (11).(11 + 3.6364)/2 = 7.3182 (new guess)

Calculate the error by subtracting the previous value from the new guess.|7.3182 – 11| = 3.68183.6818 > 0.001

Repeat this step again as the margin of error is greater than than 0.001

4

Next, we need to divide 40 by the result of the previous step (7.3182).40/7.3182 = 5.4658

Calculate the arithmetic mean of this value (5.4658) and the result of step 3 (7.3182).(7.3182 + 5.4658)/2 = 6.392 (new guess)

Calculate the error by subtracting the previous value from the new guess.|6.392 – 7.3182| = 0.92620.9262 > 0.001

Repeat this step again as the margin of error is greater than than 0.001

5

Next, we need to divide 40 by the result of the previous step (6.392).40/6.392 = 6.2578

Calculate the arithmetic mean of this value (6.2578) and the result of step 4 (6.392).(6.392 + 6.2578)/2 = 6.3249 (new guess)

Calculate the error by subtracting the previous value from the new guess.|6.3249 – 6.392| = 0.06710.0671 > 0.001

Repeat this step again as the margin of error is greater than than 0.001

6

Next, we need to divide 40 by the result of the previous step (6.3249).40/6.3249 = 6.3242

Calculate the arithmetic mean of this value (6.3242) and the result of step 5 (6.3249).(6.3249 + 6.3242)/2 = 6.3246 (new guess)

Calculate the error by subtracting the previous value from the new guess.|6.3246 – 6.3249| = 0.00030.0003

Result ✅ We found the result: 6.3246 In this case, it took us six steps to find the result.