Architecture

# What Is The Square Root Of 50 Simplified Radical Form? Simplify Square Root Of 50

The square root of 50 is a number which when multiplied by itself results in 50. Finding the square root of a number is extremely important for finding the side length of a square from its area. We will now look at how to find the value of the square root of 50 and solve some problems to help give you a better understanding.

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Square Root of 50: √50 = 7.0710678…Square of 50: 502 = 2500

 1 What is the Square Root of 50? 2 Is the Square Root of 50 Rational or Irrational? 3 How to Find the Square Root of 50? 4 Challenging Questions 5 FAQs on Square Root of 50

## What is the Square Root of 50?

The square root of a number is a number which when multiplied by itself, results in the original number. For example, the square root of 25 is 5, as 5 times 5 results in 25. However, you can also have square roots of some numbers that do not result in whole numbers, such as 50. We can express the square root of 50 in different ways:

Decimal form: 7.071Radical form: √50 = 5√2Exponent form: 501/2

## Is the Square Root of 50 Rational or Irrational?

Looking at the decimal form of the root 50, we see that it is never ending: √50 = 7.0710678118…….Therefore, we can conclude that Square Root of 50 is Irrational.

## How to find the Square Root of 50?

There are 2 main methods we use to find the Square Root of 50:

Prime Factorization

### Prime Factorization

50 = 2 × 5 × 5

Next, this can be reduced further to 50 = 2 × 52Finally, to find the root of this from here it is very easy,

√50 = √(25 × 2) = 5√2 = 5 × 1.414 = 7.07

Therefore, the Square Root of 50 ≅ 7.07

### Long Division

Step 1: Place a bar over the digits 50. We also pair the 0s in decimals in pairs of 2 from left to right.Step 5: The next divisor will be 140 + 0 and dividend will be 10000. We continue doing the same steps till we get the number of decimals we require.

So our long division now looks like this:

Therefore, the Square Root of 50 is 7.071

Explore Square roots using illustrations and interactive examples

Challenging Questions

What is the square root of 450?Is -7.071 a root of 50? If yes, why?Find the square root of: 0.5500000

## Square Root of 50 Solved Examples

Example 1: Kevin wants to buy a square plot which is 50 square feet in area. He plans on fencing the area and wants to calculate the cost of doing so. If the cost per mile of fencing is 40 dollars, find the cost of fencing the entire perimeter of the plot?

Solution:

First, to calculate the cost of fencing we would need the perimeter of the land.To find the perimeter, we need to find the side length first.Side length is the square root of area for a square.

Therefore, side length here will be √50 = 7.071, and perimeter 4 times this.Hence, the total cost of fencing = 4 × 7.071 × 40 = \$1131.36.

Example 2: Randal is travelling down the highway at an average speed of 5√50 mi/hr for half an hour. How much distance does he cover?

Solution:

We need to use the formula Distance = Speed × TimeSpeed = 5√50 = 35.355 mi/hrTime = 0.5 hrUsing the formula, Distance = 35.355 × 0.5 = 17.677Therefore, Micheal covers a distance of 17.677 miles.

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## Interactive Questions

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## FAQs on Square Root of 50

### What is the square root of 50?

The square root of 50 is √50 = 7.071.

### What is the square of 50?

The square of 50 is 502 = 2500.

### What is the square root of 50 simplified?

The square root of 50 in simplified form is 5√2.

### Is the square root of 50 a rational number?

The square root of 50 is an irrational number as it is non-terminating. It cannot be expressed in the form p/q which is what makes a rational number.