Square & Square Root of 90

Last Updated: April 28, 2024

Square & Square Root of 90

Square of 90

90² (90×90) = 8100

The square of 90, denoted as 90², equals 8100. To calculate it, you multiply 90 by itself. This operation reveals that 90 times 90 results in 8100, illustrating a basic concept in algebra where squaring a number means raising it to the power of two. Visually, if you imagine a square with each side measuring 90 units, the total area of that square would be 8100 square units. This concept is fundamental in mathematics, especially in geometry, where understanding squares helps in calculating areas and in various other applications where square values are used.

Square Root of 90

√90​ = 9.48683298051

The square root of 90, denoted as √90, is approximately 9.4868. To compute it, you find the number which, when multiplied by itself, results in 90. In mathematical terms, finding the square root involves determining the number that, when raised to the power of 2, equals the original number. Visually, you can represent the square root of 90 as a square with sides of length approximately 9.4868 units, where the area of the square is 90 square units. Understanding square roots is crucial in various mathematical disciplines and real-world applications, such as geometry, algebra, and in scenarios where you need to determine the original dimensions from an area measurement. In practical situations, knowing the square root of 90 is useful for calculations involving the extraction of original quantities from squared values.

Square Root of 90: “9.48683298051”

Exponential Form: 90^1/2 or 90^0.5

Radical Form: √90

Is the Square Root of 90 Rational or Irrational?

The square root of 90 is irrational

This is because 90 cannot be expressed as the square of a rational number. In mathematical terms, an irrational number is one that cannot be written as a simple fraction a/b​, where a and b are integers and b is not zero. The decimal expansion of an irrational number is non-repeating and non-terminating, and since no integer squared gives 90, √90 must be irrational.

Methods to Find Value of Root 90

Finding the value of the square root of 90 (√90) can be done through various methods, each suitable for different levels of precision and contexts:

1. Estimation

This method involves guessing and checking. You might start by recognizing that 92=8192=81 and 102=100102=100, placing √90 between 9 and 10. Fine-tune your estimate based on these bounds.

2. Using a Calculator

For most practical purposes, using a calculator is the quickest and most accurate method. Simply enter 90 and press the square root button to get an immediate and precise decimal value.

3. Long Division Method

This traditional method involves a step-by-step manual calculation that resembles long division. It can be very precise if carried out with enough decimal places, although it’s more time-consuming than using a calculator.

Square Root of 90 by Long Division Method

Calculating Square Root by Long Division Method (8)

To find the square root of 90 using the long division method, follow these simplified steps:

Initial Setup: Write 90 as 90.00 00 00, breaking it into pairs of digits after the decimal point.

First Calculation: Find a number whose square is closest to 90 without exceeding it. Since 9×9=81, use 9. Subtract 81 from 90 to get a remainder of 9.

Extend the Division: Bring down the next pair of zeros, making the new dividend 900.

New Divisor Setup: Double the initial quotient (9), which is 18, and use it as the start of your new divisor (180).

Refine the Divisor: Find a digit to add to 180 to form a new divisor (184) such that 184×4=736 is as close as possible to 900 without exceeding it. Subtract 736 from 900 to get 164.

Repeat the Process: Bring down the next pair of zeros, making 16400 the new dividend. Continue this process, refining the quotient and divisor until the desired precision (three decimal places) is achieved.

Result: After these steps, the approximate square root of 90 is 9.486.

90 is Perfect Square root or Not

No, 90 is not a perfect square

A perfect square is a number that can be expressed as the square of an integer. The square roots of 90 are not integers.


What two integers are the square root of 90?

The square root of 90 lies between two integers: 9 and 10. Since 9²=81 and 10²=100, √90 is approximately 9.486, positioned between these two values.

Is the square root of 90 a real number?

Yes, the square root of 90 is a real number. It is an irrational number that can be approximately expressed but cannot be exactly represented as a simple fraction.

Is 90 a cube root?

No, 90 is not a cube root. A cube root is a number that, when cubed (multiplied by itself three times), equals a given number. 90 does not fit this definition.

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