Exercises: Square Roots by Prime Factorisation

Work through each section in order. Use prime factorisation and the pairing method to find square roots, and verify each answer by squaring it.

Grade 7·17 problems·~28 min·Uganda NCDC Primary 7 Mathematics·lesson·operations-05

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What is $\sqrt{64}$ ?

$8$

$32$

$16$

$6$

Find $\sqrt{81}$ .

The perfect square $36$ can be written as $2^2 \times 3^2$ . Use this to find $\sqrt{36}$ .

$Prime factors 2, 2, 3, 3, 5, 5 with each identical pair circled, one factor taken from each pair, multiplied to give 30$

Find $\sqrt{900}$ by prime factorisation. ( $900 = 2^2 \times 3^2 \times 5^2$ .)

Find $\sqrt{5929}$ , given that $5929 = 7^2 \times 11^2$ .

$77$

$18$

$121$

$88$

Find $\sqrt{441}$ by prime factorisation, then verify your answer by squaring it. ( $441 = 3^2 \times 7^2$ .)

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