Combining like square roots Practice Questions (Grade 9)

Warm-upeasy

Which expression is equivalent to $\sqrt{72}+\sqrt{98}$ ?

$\sqrt{72}=\sqrt{36 \cdot 2}=6\sqrt{2}$ and $\sqrt{98}=\sqrt{49 \cdot 2}=7\sqrt{2}$ . Adding like radical terms gives $6\sqrt{2}+7\sqrt{2}=13\sqrt{2}$ .

Mid-gameeasy

Which expression is equivalent to $\sqrt{80}+\sqrt{45}$ ?

$\sqrt{80}=\sqrt{16 \cdot 5}=4\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$ . Adding like radical terms gives $4\sqrt{5}+3\sqrt{5}=7\sqrt{5}$ .

Mid-gameeasy

Which expression is equivalent to $\sqrt{54}+\sqrt{24}$ ?

$\sqrt{54}=\sqrt{9 \cdot 6}=3\sqrt{6}$ and $\sqrt{24}=\sqrt{4 \cdot 6}=2\sqrt{6}$ . Adding like radical terms gives $3\sqrt{6}+2\sqrt{6}=5\sqrt{6}$ .

Mid-gameeasy

Which expression is equivalent to $\sqrt{108}+\sqrt{147}$ ?

$\sqrt{108}=\sqrt{36 \cdot 3}=6\sqrt{3}$ and $\sqrt{147}=\sqrt{49 \cdot 3}=7\sqrt{3}$ . Adding like radical terms gives $6\sqrt{3}+7\sqrt{3}=13\sqrt{3}$ .

Mid-gamemedium

Which expression is equivalent to $\sqrt{27}+\sqrt{48}+\sqrt{75}$ ?

$\sqrt{27}=3\sqrt{3}$ , $\sqrt{48}=4\sqrt{3}$ , and $\sqrt{75}=5\sqrt{3}$ . Adding gives $3\sqrt{3}+4\sqrt{3}+5\sqrt{3}=12\sqrt{3}$ .

Mid-gamemedium

Which expression is equivalent to $\sqrt{18}+\sqrt{50}+\sqrt{32}$ ?

$\sqrt{18}=3\sqrt{2}$ , $\sqrt{50}=5\sqrt{2}$ , and $\sqrt{32}=4\sqrt{2}$ . Adding gives $3\sqrt{2}+5\sqrt{2}+4\sqrt{2}=12\sqrt{2}$ .

Mid-gamemedium

Which expression is equivalent to $3\sqrt{20}+\sqrt{45}$ ?

$3\sqrt{20}=3\sqrt{4 \cdot 5}=3 \cdot 2\sqrt{5}=6\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$ . Adding like radical terms gives $6\sqrt{5}+3\sqrt{5}=9\sqrt{5}$ .

Buzzer beatermedium

Which expression is equivalent to $\sqrt{28}+\sqrt{63}+\sqrt{7}$ ?

$\sqrt{28}=2\sqrt{7}$ , $\sqrt{63}=3\sqrt{7}$ , and $\sqrt{7}=\sqrt{7}$ . Adding gives $2\sqrt{7}+3\sqrt{7}+\sqrt{7}=6\sqrt{7}$ .

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