Question

The value of $(5^{\frac{1}{2}}+3^{\frac{1}{2}})(5^{\frac{1}{2}}-3^{\frac{1}{2}})$ is:

• A. $2$
• B. $3$
• C. $5$
• D. $1$

Answer 1

The correct option is A $2$

Given, $(5^{\frac{1}{2}}+3^{\frac{1}{2}})(5^{\frac{1}{2}}-3^{\frac{1}{2}})$.

We know, $(a+b)(a-b)=a^2-b^2$.

Then,

$(5^{\frac{1}{2}}+3^{\frac{1}{2}})(5^{\frac{1}{2}}-3^{\frac{1}{2}})$

$=5^{\frac{1}{2}\times 2}-3^{\frac{1}{2}\times 2}$

$=5^1-3^1$

$=5-3$

$=2$.

Hence, option $A$ is correct.