Question

$4 \sqrt{28x} + \sqrt{63x = }$what are the steps to solving this?

Answer 1

We are given the following radical expression

$4\sqrt[]{28z}+\sqrt[]{63z}$

Let us simplify the expression.

Re-write the radicals as

$4\sqrt[]{28z}+\sqrt[]{63z}=4\sqrt[]{4\cdot7z}+\sqrt[]{9\cdot7z}$

Apply the product rule below

$\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}$

So applying the above rule, the expression becomes

$4\sqrt[]{4\cdot7z}+\sqrt[]{9\cdot7z}=4\sqrt[]{4}\cdot\sqrt[]{7z}+\sqrt[]{9}\cdot\sqrt[]{7z}$

We know that 4 and 9 are perfect squares so the expression becomes

$4\sqrt[]{4}\cdot\sqrt[]{7z}+\sqrt[]{9}\cdot\sqrt[]{7z}=4\cdot2\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}=8\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}$

Finally, Combine the radicals

$8\cdot\sqrt[]{7z}+3\cdot\sqrt[]{7z}=(8+3)\sqrt[]{7z}_{}=11\sqrt[]{7z}$

Therefore, the simplified expression is

$11\sqrt[]{7z}$