Question

select all that are like radicals after simplifying. \\(\sqrt{50x^2}\\) \\(\sqrt{32x}\\) \\(\sqrt{18n}\\) \\(\sqrt{72x^2}\\) done

Explanation:

Step1: Simplify $\sqrt{50x^2}$

Factor into perfect squares:
$\sqrt{50x^2} = \sqrt{25 \cdot 2 \cdot x^2} = \sqrt{25x^2} \cdot \sqrt{2} = 5x\sqrt{2}$

Step2: Simplify $\sqrt{32x}$

Factor into perfect squares:
$\sqrt{32x} = \sqrt{16 \cdot 2x} = \sqrt{16} \cdot \sqrt{2x} = 4\sqrt{2x}$

Step3: Simplify $\sqrt{18n}$

Factor into perfect squares:
$\sqrt{18n} = \sqrt{9 \cdot 2n} = \sqrt{9} \cdot \sqrt{2n} = 3\sqrt{2n}$

Step4: Simplify $\sqrt{72x^2}$

Factor into perfect squares:
$\sqrt{72x^2} = \sqrt{36 \cdot 2 \cdot x^2} = \sqrt{36x^2} \cdot \sqrt{2} = 6x\sqrt{2}$

Step5: Identify like radicals

Like radicals have identical radicands (the expression under the square root). $\sqrt{50x^2}$ and $\sqrt{72x^2}$ both simplify to have $\sqrt{2}$ as the radical part.

Answer:

• $\boldsymbol{\sqrt{50x^2}}$
• $\boldsymbol{\sqrt{72x^2}}$