Squares & Square Roots

12 Grade 8 Mathematics questions on Squares & Square Roots, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   Work out: $0.3^2$

   A. 0.6

   B. 0.9

   C. 0.09

   D. 0.03

   (1 mark)

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2. Question 2

   1 mark

   Find: $\sqrt{625}$

   A. 25

   B. 35

   C. 15

   D. 312.5

   (1 mark)

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3. Question 3

   1 mark

   Find: $\sqrt{324}$

   A. 18

   B. 16

   C. 162

   D. 17

   (1 mark)

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4. Question 4

   1 mark

   Work out: $\sqrt{64}+\sqrt{36}$

   A. 10

   B. 100

   C. 50

   D. 14

   (1 mark)

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5. Question 5

   1 mark

   Work out: $2.5^2$

   A. 5

   B. 6.5

   C. 4.25

   D. 6.25

   (1 mark)

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6. Question 6

   1 mark

   Work out: $\sqrt{196}+\sqrt{121}$

   A. 25

   B. 23

   C. 27

   D. 15

   (1 mark)

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7. Question 7

   3 marks

   The area of a square is 400 cm². Find its perimeter.

   (3 marks)

   Marking scheme

   The area of a square is side $\times$ side, so the side is the square root of the area. (1)

   $\sqrt{400}=20$ cm. (1)

   The perimeter is $4\times$ side $=4\times 20=80$. (1)

   Final answer: $80$ cm.

8. Question 8

   1 mark

   What is the square of 14?

   A. 28

   B. 196

   C. 144

   D. 169

   (1 mark)

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9. Question 9

   3 marks

   Evaluate: $\sqrt{169}+8^2-\sqrt{81}$

   (3 marks)

   Marking scheme

   Work out each root and power first, before adding or subtracting. (1)

   $\sqrt{169}=13$, $8^2=64$ and $\sqrt{81}=9$. (1)

   Now work left to right: $13+64=77$, then $77-9=68$. (1)

   Final answer: $68$.

10. Question 10

    3 marks

    The area of a square garden is 256 m squared.

    (a) Find the length of one side. (1 mark)

    (b) Find the perimeter of the garden. (2 marks)

    Marking scheme

    (a) The area of a square is side $\times$ side, so the side is $\sqrt{256}=16$ m. (1)

    (b) A square has four equal sides, so the perimeter is $4\times$ side. (1)

    $4\times 16=64$. (1)

    Final answer: (a) $16$ m (b) $64$ m.

11. Question 11

    1 mark

    The area of a square is 169 cm squared. What is the length of one side?

    A. 84.5 cm

    B. 13 cm

    C. 13.5 cm

    D. 12 cm

    (1 mark)

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12. Question 12

    1 mark

    Find: $\sqrt{\frac{1}{16}}$

    A. $\frac{1}{8}$

    B. $\frac{1}{16}$

    C. $\frac{1}{4}$

    D. $\frac{1}{2}$

    (1 mark)

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