# Square Root and Cube Root

Square Root and Cube Root Concepts is used in almost every topic of mathematics. So, candidates can learn Square Root and Cube Root Elementary Algebra solving techniques, symbol, formula, tricks etc from this page. Also, Square Root and Cube Root Table PDF is also shared here that will be useful for the candidates during preparation of competitive examination and can help in solving the question in time.

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## Square Root and Cube Root

Square Root and Cube Root Symbol:

The square root is denoted by the symbol ‘√’, whereas the cube root is denoted by ‘∛’.

Examples:

√4 = √(2 × 2) = 2

∛27 = ∛(3 × 3 × 3) = 3

Square Root and Cube Root Chart:

 Number Square root (√) Cube root (∛) 1 1.000 1.000 2 1.414 1.260 3 1.732 1.442 4 2.000 1.587 5 2.236 1.710 6 2.449 1.817 7 2.646 1.913 8 2.828 2.000 9 3.000 2.080 10 3.162 2.154 11 3.317 2.224 12 3.464 2.289 13 3.606 2.351 14 3.742 2.410 15 3.873 2.466

Square Root Formula:

When a value is multiplied by itself to give the original number then that number is a square root. Square Root is represented by the symbol √. For example, 4 and -4 are the square roots of 16.

The formula to represent the square root is given below: Solved Example: What is the square root of 144?

Solution:

The factors of 144 are given as,

144 = 12×12

√144 =√12×12

√144= 12

Solved Example: What is the square root of 80?

Solution:

The factors of 80 are given as,

80= 4×4×5

√80 =√4×4×5

√80=4√5

Cube Root Definition:

The cube root of any number say ‘a’, is the number ‘b’, which satisfy the equation given below:

b= a

This can be represented as:

a = ∛b

Cube Root Formula:

The cube root formula is used to give the cube root value of any number.

For Example:

5 Cube = 53 = 125
Cube Root of 125 = 3√125 = 5

Thus, the cube root of 125 is 5.

Solved Example: What is the cube root of 1728?

Solution:

The factors of 1728 are given as,

1728 = 12 × 12 × 12

3√1728 = 3√(12 × 12 × 12)

3√1728 = 12

Cube Root by Prime Factorisation Method:

We can find the cube-root of a number by the method of prime factorisation.

For Example:

2744= 2 × 2× 2 × 7 ×7 × 7= (2 × 7 )3

Therefore, the cube root of 2744 = ∛2744 = 2 × 7 = 14

Solve Here: Chain Rule Aptitude Questions and Answers

Easy Tricks to Find Square Roots and Cube Roots:

Finding Square Root:

Above 100:

1032 = 10609

Step 1. Add the number to the ones digit:
103 + 3 = 106
Step 2. Square the ones digit number (if the result is a single digit put a 0 in front of it):
32 = 09
Step 3. Place the result from Step 2 next to the result from Step 1: 10609

Below 100:

972 = 9409

Step 1. Subtract the number from 100: 100- 97 = 3

Step 2. Subtract the number (from Step 1) from original number : 97-3 =94

Step 3. Square the result from Step 1 (if the result is a single digit put a 0 in front of it): 3= 09

Step 4. Place the result from Step 3 next to the result from Step 2: 9409

Below 50:

482 = 2304

Step 1. Subtract the number from 50: 50-48=2

Step 2. Subtract the result (from Step 1) from 25: 25-2 =23

Step 3. Square the result from Step 1 if the result is a single digit put a 0 in front of it ) : 22 = 04

Step 4. Place the result from Step 3 next to the result from Step 2: 2304

Above 50:

532 = 2809

Step 1. Add 25 to the ones digit: 25 + 3 = 28

Step 2. Square the ones digit number ( if the result is a single digit put a 0 in front of it ) : 32 = 09

Step 3. Place the result from Step 2 next to the result from Step 1 : 2809

Finding Cube Root:

Remembering Units Digits:

Remember cubes of 1 to 10 and unit digits of these cubes.

1 = 1

2 = 8

3 = 7

4 = 4

5 = 5

6 = 6

7 = 3

8 = 2

9 = 9

10 = 0

Whenever unit digit of a number is 9, the unit digit of the cube of that number will also be 9. Similarly, if the unit digit of a number is 9, the unit digit of the cube root of that number will also be 9.

Deriving Cube Root From Remaining Digits

Find the cube root of 474552.

Unit digit of 474552 is 2. So we can say that unit digit of its cube root will be 8.

Now we find cube root of 447552 by deriving from remaining digits.

Let us consider the remaining digits leaving the last 3 digits. i.e. 474.

Since 474 comes in between cubes of 7 and 8.

So the ten’s digit of the cube root will definitely be 7

i.e. cube root of 474552 will be 78.

Solve Here: Number Series Question

Properties of Square Root:

• If the unit digit of a number is 2, 3, 7, and 8 then its square root is not a natural number.
• If a number ends in an odd number of zeros, then its square root is not a natural number.
• The square root of an even number is even and that of an odd number is odd.
• Negative numbers have no squares root in a set of real numbers.

Properties of Cube Root:

• Cube root of all the odd numbers is an odd number.
• Cube root of all the even natural numbers is even.
• The cube root of a negative integer always results in negative.

The details mentioned above about Square Root and Cube Root Topic is well written by the team members of reruitmentresult.com Individuals must go through it and prepare well for their examination.

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