Question

how many largest perfect squares are under each radical?
radical | largest perfect squares
\\(sqrt{8}\\) |
\\(sqrt{18}\\) |
\\(sqrt{32x^6}\\) |
\\(sqrt{50x}\\) |
\\(sqrt{72}\\) |

Explanation:

Step1: Factor √8, find largest square

$8 = 4 \times 2$, where $4=2^2$

Step2: Factor √18, find largest square

$18 = 9 \times 2$, where $9=3^2$

Step3: Factor √32x⁶, find largest square

$32x^6 = 16x^6 \times 2$, where $16x^6=(4x^3)^2$

Step4: Factor √50x, find largest square

$50x = 25 \times 2x$, where $25=5^2$

Step5: Factor √72, find largest square

$72 = 36 \times 2$, where $36=6^2$

Answer:

Radical	Largest perfect squares
$\sqrt{18}$	$9$
$\sqrt{32x^6}$	$16x^6$
$\sqrt{50x}$	$25$
$\sqrt{72}$	$36$