Squares & Square Roots

10 Grade 7 Mathematics questions on Squares & Square Roots, with worked marking schemes. 10 questions are available on this topic in full.

1. Question 1

   2 marks

   A square field has an area of 1,296 m². Find the length of one side.

   (2 marks)

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2. Question 2

   3 marks

   Find the square root of 2,025 by factorisation.

   (3 marks)

   Marking scheme

   Break $2025$ into prime factors: $2025=5\times 405$, and $405=5\times 81$, so $2025=5\times 5\times 81$. (1)

   Since $81=9\times 9$, this is $2025=5^2\times 9^2$ — every factor appears in a pair. (1)

   A square root takes one from each pair: $\sqrt{2025}=5\times 9=45$. (1)

   Final answer: $45$. Check: $45\times 45=2025$.

3. Question 3

   1 mark

   What is $0.04^2$?

   A. 0.0016

   B. 0.008

   C. 0.08

   D. 0.16

   (1 mark)

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4. Question 4

   1 mark

   Find $\sqrt{225}$.

   A. 25

   B. 16

   C. 14

   D. 15

   (1 mark)

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5. Question 5

   3 marks

   Evaluate without a calculator: $\sqrt{0.0049}$

   (3 marks)

   Marking scheme

   Write the decimal as a fraction so both parts are perfect squares: $0.0049=\frac{49}{10000}$. (1)

   The square root of a fraction is the square root of the top over the square root of the bottom: $\frac{\sqrt{49}}{\sqrt{10000}}=\frac{7}{100}$. (1)

   $\frac{7}{100}=0.07$. (1)

   Final answer: $0.07$. Check: $0.07\times 0.07=0.0049$.

6. Question 6

   1 mark

   Evaluate: $\sqrt{81}+\sqrt{49}$

   A. 12

   B. 130

   C. 16

   D. 14

   (1 mark)

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7. Question 7

   1 mark

   What is 13²?

   A. 144

   B. 196

   C. 169

   D. 156

   (1 mark)

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8. Question 8

   1 mark

   Evaluate: $\sqrt{\frac{16}{25}}$

   A. $\frac{4}{25}$

   B. $\frac{4}{5}$

   C. $\frac{2}{5}$

   D. $\frac{16}{5}$

   (1 mark)

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9. Question 9

   2 marks

   Evaluate: $\sqrt{324}-\sqrt{144}$

   (2 marks)

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10. Question 10

    1 mark

    Find $\sqrt{1.44}$.

    A. 1.44

    B. 0.12

    C. 1.2

    D. 12

    (1 mark)

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