Squares and Square Roots mathematical comprehension is essential. These ideas are essential for students in all grades and serve as the foundation for more complex subjects.

In this article, we have covered Square and Square Roots, its practice questions and others in detail.

What are Square and Square Roots?

A Square of a number is the result of multiplying that number by itself. It can be written mathematically as n² where n is the number. The square of 4, for instance, is 4² = 16. When the number is an integer, squares are sometimes referred to as perfect squares. The geometric property that gives the area of a square, or a four-sided object with equal sides, is the square of the side length is where the term “Square” originates.

Example: Calculate the square of 7.

7² = 7 × 7

= 49

Square Roots are the values that multiplies by itself to return the original number is called the square root of a number. [Tex]\sqrt{}[/Tex] ​is the radical symbol used to represent it. For example, the square root of 36 is √36 = 6 because 6 × 6 = 36. Given that the square roots of 36 are 6 and −6 , they can be either positive or negative.

The major square root, however, is usually regarded as the positive square root in most situations.

Example: Find the square root of 16.

√16 = √(4×4)

Important Related Formulas/Concepts

Square of a Number

n² = n × n {Let ‘n’ be any number where N}

Square Root of a Number

√n × √n = n {Let ‘n’ be any number where N}

Square and Square Roots Practice Questions

Question 1. What is the square of 6?

Solution:

Square of 6 is

6² = 6 × 6

= 36

Question 2. Calculate the square root of 64.

Solution:

Square root of 64 is

√64 = 8

Because, 8 × 8 = 64

Question 3. Find the square of 13.

Solution:

Square of 13 is

13² = 13 × 13

= 169

Question 4. What is the square of -5?

Solution:

Square of -5 is

(-5)² = -5 × -5

= 25

Question 5. Find the value of √50.

Solution:

Prime factor of 50 is

50 = 5 × 5 × 2

Square root of 50 is √50 = 5√2

Question 6. Find the value of 27² using identity.

Solution:

27² = (30 – 3)² = 30² – 2 × 30 × 3 + 3²

= 900 – 180 + 9

= 909 – 180 = 729

Question 7. Calculate the square root of 121.

Solution:

Square root of 121 is

√121 = 11

Because, 11 × 11 = 121

Worksheet on Square and Square Roots

Q1. Find the square of 8.

Q2. What is the square root of 144?

Q3. Calculate the square of -9.

Q4. Determine the square root of 1.44.

Q5. If x² = 361, find x.

Q6. Find the square of 20.

Q7. What is the square root of 64?

Q8. Calculate the square of 0.5.

Q9. Determine the square root of 0.36.

Q10. If z² = 225, find z.

Read More:

• Squares and Square Roots
• Square root of a Number 
• Square Root of an Integer
• Square Root

Frequently Asked Questions

What is Difference between a square and a square root?

A number can be made square by multiplying it by itself, but a square root is a value that yields the original number when multiplied by itself.

For a negative number, what is its square?

The square of a negative number is positive.

Can Negative Square Roots Exist?

Yes, negative square roots are possible. The square roots of 9 are 3 and -3.

How to Find Square Root of a Decimal?

To find the square roots of the numerator and denominator independently, convert the decimal to a fraction. If needed, return the fraction to decimal form.

What are Practical Applications of Squares and Square Roots?

Architecture, physics, engineering, and other professions all make use of them. solving quadratic equations, for example, and calculating areas and building structures.