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Squares and square roots
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EasyQuestion 1
[2 marks]Work out:
(a) 13²
(b) √144
Solution for Question 1
MediumQuestion 2
[3 marks]Without using a calculator:
(a) Estimate √75 to one decimal place.
(b) Explain your method.
Solution for Question 2
HardQuestion 3
[3 marks]Simplify fully: √(2² × 3⁴ × 5²)
Solution for Question 3
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A square number is the result of multiplying a number by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... You should memorise squares up to 15² = 225 for your GCSE exam.
The square root is the inverse operation - it asks "what number multiplied by itself gives this?" The symbol √ means the positive square root. Every positive number has two square roots (positive and negative), but √ refers only to the positive one.
For non-perfect squares, estimate by finding which perfect squares it lies between. For example, √50 lies between √49 = 7 and √64 = 8, closer to 7 since 50 is closer to 49. More precisely, √50 ≈ 7.07.
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