Question

Evaluate:

(1) $4^{\frac{1}{2}}$
(2) ${125}^{\frac{1}{3}}$
(3) $1^{\frac{1}{2}}$
(4) $1^{\frac{1}{3}}$
(5) ${100}^{\frac{1}{2}}$
(6) ${1000}^{\frac{1}{3}}$
(7) ${225}^{\frac{1}{2}}$
(8) ${512}^{\frac{1}{3}}$
(9) ${64}^{\frac{1}{2}}$
(10) ${64}^{\frac{1}{6}}$

Answer 1

(1) $4^{\frac{1}{2}}$ can be written as the square root of 4.
And 4 = 2 × 2
So, square root of 4 = 2
$\therefore 4^{\frac{1}{2}}=\sqrt{4}=2$

(2) ${125}^{\frac{1}{3}}$ can be written as the cube root of 125.
And 125 = 5 × 5 × 5
So, cube root of 125 = 5
$\therefore {125}^{\frac{1}{3}}=\sqrt[3]{125}=5$

(3) $1^{\frac{1}{2}}$ can be written as the square root of 1.
And 1 = 1 × 1
So, square root of 1 = 1
$\therefore 1^{\frac{1}{2}}=\sqrt{1}=1$

(4) $1^{\frac{1}{3}}$can be written as the cube root of 1.
And 1 = 1 × 1× 1
So, cube root of 1 = 1
$\therefore 1^{\frac{1}{3}}=\sqrt[3]{1}=1$

(5) ${100}^{\frac{1}{2}}$ can be written as the square root of 100.
And 100 = 10 × 10
So, square root of 100 = 10
$\therefore {100}^{\frac{1}{2}}=\sqrt{100}=10$

(6) ${1000}^{\frac{1}{3}}$ can be written as the cube root of 1000.

And 1000 = 10 × 10 × 10
So, cube root of 1000 = 10
$\therefore {1000}^{\frac{1}{3}}=\sqrt[3]{1000}=10$

(7) ${225}^{\frac{1}{2}}$ can be written as the square root of 225.
And 225 = 15 × 15
So, square root of 225 = 15
$\therefore {225}^{\frac{1}{2}}=\sqrt{225}=15$

(8) ${512}^{\frac{1}{3}}$ can be written as the cube root of 512.
And 512 = 8 × 8 × 8
So, the cube root of 512 = 8
$\therefore {512}^{\frac{1}{3}}=\sqrt[3]{512}=8$

(9) ${64}^{\frac{1}{2}}$ can be written as the square root of 8.
And 64 = 8 × 8
So the square root of 64 = 8
$\therefore {64}^{\frac{1}{2}}=\sqrt{64}=8$

(10) ${64}^{\frac{1}{6}}$ can be written as the sixth root of 64.
And 64 = 2 × 2 × 2 × 2 × 2 × 2
So the sixth root of 64 = 2
$\therefore {64}^{\frac{1}{6}}=\sqrt[6]{64}=2$