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Square Root of 70

The square root of 70 is expressed as √70 in the radical form and as (70)^½ or (70)^0.5 in the exponent form. The square root of 70 rounded up to 10 decimal places is 8.3666002653. It is the positive solution of the equation x² = 70.

Square Root of 70: 8.366600265340756
Square Root of 70 in exponential form: (70)^½ or (70)^0.5
Square Root of 70 in radical form: √70

1.	What Is the Square Root of 70?
2.	Is Square Root of 70 Rational or Irrational?
3.	How to Find the Square Root of 70?
4.	Important Notes
5.	FAQs on Square Root of 70
6.	Challenging Questions

What Is the Square Root of 70?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 70 can be written in multiple ways

Radical form: √70
Decimal form: 8.366
Exponent form: (70)^1/2

Is Square Root of 70 Rational or Irrational?

70 is a number which is not a perfect square, which means it does not have a natural number as its square root.
Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 70 is an irrational number.

How to Find the Square Root of 70?

There are multiple ways to find the square root of 70-

Long Division Method
Estimation and Approximation

One can find out more about these methods by clicking here.

Long Division Method

The square root of 70 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits 70 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 70. The number 8 fits here as 8 square gives 64. Dividing 70 by 8 with quotient as 8, we get the remainder as 6.
Step 3: Drag a pair of 0s down and fill it next to 6 to make the dividend 600.
Step 4: Double the divisor 8, and enter 16 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 16X × X results in a value less than or equal to 600. This will be 3 in this case, so divide 600 with 163 and write the remainder.
Step 5: Repeat this process to get the decimal places you want.

Square Root of 70

Therefore, the square root of 70 = 8.366

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

First, we will find the two consecutive numbers such that 70 lies between their perfect squares.
In this case, the numbers are 8 (64) and 9 (81).
We take the whole number part to be the smaller perfect square, in this case, 8.
Now, for the decimal part we will use the below formula:
(Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
= (70 - 64)/(81 - 64) = 6/17 = 0.35
Therefore, we can estimate the square root of 70 ≅ 8.35

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Important Notes

The square root of 70 is an irrational number that is non-terminating.
There will be n/2 digits in the square root of an even number with n digits.
There will be (n+2)/2 digits in the square root of an odd number with n digits.
The square root of -70 is an imaginary number.

Challenging Questions

What is the square root of 75 up to 5 decimal places? (Use long division)
Find the square root of the following numbers:
- 490000
- 0.70

Solved Examples

Example 1: What is the square root of -√70?

Solution:

The square root of negative numbers is represented by imaginary numbers.
So, the square root of -√70 is written as √70 i. Where (i = -√1)
Example 2: Richard wants to buy a new wheel for his car. At the store, he finds a wheel that has an area of 4900π sq cm. What is the radius of the wheel?

Solution:

To find the radius of the wheel, we have to use the formula, πr².
πr² = 4900π
r² = 4900
r = 70

Therefore, the radius of the wheel is equal to 70 cm
Example: If the area of a square is 70 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 70 in²
⇒ a = ±√70 in
Since length can't be negative,
⇒ a = √70 = 8.367 in

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FAQs on the Square Root of 70

What is the Value of the Square Root of 70?

The square root of 70 is 8.3666.

Why is the Square Root of 70 an Irrational Number?

Upon prime factorizing 70 i.e. 2¹ × 5¹ × 7¹, 2 is in odd power. Therefore, the square root of 70 is irrational.

What is the Square of the Square Root of 70?

The square of the square root of 70 is the number 70 itself i.e. (√70)² = (70)^2/2 = 70.

If the Square Root of 70 is 8.367. Find the Value of the Square Root of 0.7.

Let us represent √0.7 in p/q form i.e. √(70/100) = 0.7/10 = 0.837. Hence, the value of √0.7 = 0.837

Evaluate 12 plus 18 square root 70

The given expression is 12 + 18 √70. We know that the square root of 70 is 8.367. Therefore, 12 + 18 √70 = 12 + 18 × 8.367 = 12 + 150.599 = 162.599

What is the Square Root of -70?

The square root of -70 is an imaginary number. It can be written as √-70 = √-1 × √70 = i √70 = 8.366i
where i = √-1 and it is called the imaginary unit.

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