Question

which expression represents simplest form of \\(\sqrt{40} - \sqrt{10}\\)?
a \\(\sqrt{10}\\)
b \\(\sqrt{30}\\)
c 4
d \\(2\sqrt{5}\\)

Explanation:

Step1: Simplify $\sqrt{40}$

Factor 40 into $4 \times 10$, so $\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}$

Step2: Subtract $\sqrt{10}$

Substitute the simplified term: $2\sqrt{10} - \sqrt{10} = (2-1)\sqrt{10} = \sqrt{10}$

Answer:

A. $\sqrt{10}$