Square root of 90
90 is not a perfect square, however, it is a semiperfect number which means that it is the sum of all or some of its divisors. Square root of 90 is raising 90 to the power half. In this lesson, we will calculate the square root of 90 by long division method and the approximation method and solve a few interesting problems.
 Square Root of 90: √90 = 9.486
 Square of 90: 90^{2 } = 8100
1.  What Is the Square Root of 90? 
2.  Is the Square Root of 90 Rational or Irrational? 
3.  How to Find the Square Root of 90? 
4.  FAQs on Square Root of 90 
What Is the Square Root of 90?
 The square root of a number is the number that when multiplied to itself gives the original number as the product.
 n × n = 90. This shows square of a number is 90.
 n = √90 or n = 90^{½}
 90 = 3 × 3 × 10 = 3^{2 }× 10
 Thus √90 = √(3^{2 }× 10)
 Squaring on both the sides, 90^{½ }= 3√10
 Thus the simplified form of √90 = 3√10
 The value of √90 is evaluated as 9.486832980505138
Is the Square Root of 90 Rational or Irrational?
 A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0.
 √90 = 9.486832980505138
 Therefore √90 is irrational.
How to Find the Square Root of 90?
The square root of 90 can be calculated using different methods such as prime factorization or the long division method or the average method. By the prime factorization method, we find that the simplest radical form √90 is 3√10.
Square Root of 90 by Approximation Method
 Find 2 perfect squares closest to 90. They are 81 and 100. 81 < 90 < 100
 √81 < √90 < √100
 9 < √90 < 10
 Divide 90 by 9 or 10. let's divide by 9. 90 ÷ 9 = 10
 Find the average of this quotient and the 9. (10 +9) ÷ 2
 19 ÷ 2 = 9.5
 Thus √90 ≈ 9.5
Square Root of 90 by Long Division Method
 Write 90 in pairs after the decimal point as 90. 00 00 00.
 Find a number x number that gives 90 or less than that. We find 9 × 9 = 81. subtract 81 from 90 and obtain 9 as the remainder.
 Bring down the next pair of zeros. 900 becomes the new dividend.
 Multiply the quotient obtained in the previous step with 2. It is 18. Now 180 is written in the new divisor's place.
 Find a number to be added in the unit's place with 180 such that the sum when multiplied by the number results in 900 or less than that. We determine that 180 + 4 = 184 and 184 × 4 = 736.
 Subtract this from 900. It is 164 and get the new divisor by brining down the next pair of zeros. 16400 is our new dividend.
 Repeat the process until we approximate the value to 3 decimal places.
 Thus, √90 = 9.486.
Explore Square roots using illustrations and interactive examples
Tips And Tricks
 Know that 90 lies between the perfect squares 81 and 100 and hence the square root of 90 lies between 9 and 10.
 Use the average method to approximate the square root of 90.
Important Notes
 The square root of 90 is expressed as 3√10 in the radical form and as 90^{½} in the exponential form.
 √90 = ± 9.486832980505138
Square Root of 90 Solved Examples

Example 1: Jolly wants to fence her square garden. Its area is 90 sq yards. How long will be the fence?
Solution:
The fence covers the garden which forms the perimeter of the garden.
To evaluate the perimeter, side of the garden is required.
Given area of the garden = 90 sq yards
Area = side × side
90 = side^{2}
side = √90 = 9.48 yards.
Length of the fence = 4 × 9.48 = 37.92 yards 
Example 2 : Evaluate a) √90 × √75 b) √90 + √75
Solution:
As √90 = √(9 × 10) = 3√10 and √75 = √(25 × 10) = 5√10
a) √90 × √75 = 3√10 × 5√10 = (3 × 5)(√10×√10) = 15 × 10 = 150
b) √90 + √75 = 3√10 + 5√10 = (3 + 5)√10 = 8√10
FAQs on Square Root of 90
What is the square root of 90 simplified?
The square root of 90 simplified in radical form is 3√10.
Is the square root of 90 a rational number?
No, the square root of 90 is evaluated in the decimal form as 9.486. Hence, it is irrational.
How can we calculate the square root of 90?
The √90 can be evaluated using the approximation method or using the division method.
Between which two numbers does the square root of 90 lie?
The square root of 90 lies between 9 and 10.
What is the square root of 90 rounded to the nearest tenth?
The square root of 90 rounded to the nearest tenth is 9.5.
visual curriculum