Question

`4 √(28x) + √(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}`