Q. 8.87 - Intermediate Algebra

Question

Simplify-
$(5\sqrt{3}-\sqrt{7})(3+2\sqrt{7})$

Step-by-Step Solution

Answer

The value is $15\sqrt{3}+10\sqrt{21}-3\sqrt{7}-14$.

Step 1. Given and explanation

We have $(5\sqrt{3}-\sqrt{7})(3+2\sqrt{7})$.

We will simply multiply the terms and then simplify by combining the like terms to get the value.

Step 2. Multiplying the terms and simplifying.

We have $(5\sqrt{3}-\sqrt{7})(3+2\sqrt{7})$.

Multiplying the terms give us,

$$\begin{gathered} =15\sqrt{3}+(5·2\sqrt{3·7})-3\sqrt{7}-(2·7) \\ =15\sqrt{3}+10\sqrt{21}-3\sqrt{7}-14 \end{gathered}$$

Thus we get the value as $15\sqrt{3}+10\sqrt{21}-3\sqrt{7}-14$.