Question

From the following real numbers, has its square root as an irrational numbers.

• A. 144
• B. 169
• C. 196
• D. 255

Answer 1

The correct option is D 255

Let us consider 196

$\text{Square root of 196 can be represented}$
$\text{as}\sqrt[2]{2196}=\sqrt[2]{22\times 2\times 7\times 7}=14$

which is a rational number.

Let us consider 144

$\text{Square root of 144 can be represented}$
$\text{as}\sqrt[2]{2144}=\sqrt[2]{22\times 2\times 2\times 2\times 3\times }=12$

which is a rational number.

Let us consider 169

$\text{Square root of 169 can be represented}$
$\text{as}\sqrt[2]{2169}=\sqrt[2]{213\times 13}=13$

which is a rational number.

Let us consider 255

$\text{Square root of 255 can be represented}$
$\text{as}\sqrt[2]{2196}=\sqrt[2]{23\times 5\times 17}$

which is an irrational number.

So, only 255 will have its square root as an irrational number.