Square roots and Cube roots

Square Roots

The square root of a positive number ‘n’ is that number which, when multiplied by itself, gives ‘n’.

There are two square roots for a positive number. For example, the square roots of 25 are +5 and -5. The positive square root of a number is called the principal square root.

The symbol √ is called the radical sign. The index notation is also used instead of the radical sign. For example:

$\sqrt{16}$ = +4 can be written as $16^{1/2}$ = +4 .

Example: Find the square root of 81.

81 = 9 × 9

$\sqrt{81}$ = 9

Cube Roots

The cube root of a positive number ‘N’ is that number which, when multiplied by itself twice, gives ‘N’.

For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8 (here 2 is being multiplied by itself twice)

The symbol for cube root is a radical sign with a small 3 on the left ∛ .

Example: Find the cube root of -125.

-125 = (-5)³ = -5 × -5 × -5

$\sqrt[3]{-125}$ = -5

Example: Simplify: $\sqrt[3]{343}$ – $\sqrt{196}$ + 4

7 × 7 × 7 = 343, so $\sqrt[3]{343}$ = 7

14 × 14 = 196, so $\sqrt{196}$ = 14

so , $\sqrt[3]{343}$ – $\sqrt{196}$ + 4 = 7 – 14 + 4 = 11 -14 = -3

CHECK POINT

Find the square root of 169.
What is the cube root of 1331?
Simplify: $\sqrt{225}$ + $\sqrt[3]{-729}$ – 5
Value of $\sqrt[3]{216}$ – $\sqrt[3]{-216}$
What is the square root of 1,024?

Answer key

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