Question

1. determine the value of each square root without using a calculator - leave answers as a fraction or decimal (3 marks)

a) \\(\sqrt{0.01}\\)

b) \\(\sqrt{36/121}\\)

c) \\(\sqrt{1/16}\\)

Explanation:

Evaluate the square root of the decimal in part a

Using the Square Root of Decimals knowledge point

$$ \sqrt{0.01} = \sqrt{\frac{1}{100}} = \frac{\sqrt{1}}{\sqrt{100}} = \frac{1}{10} = 0.1 $$

Evaluate the square root of the fraction in part b

To find the square root of a fraction, we can take the square root of the numerator and the square root of the denominator separately.

$$ \sqrt{\frac{36}{121}} = \frac{\sqrt{36}}{\sqrt{121}} $$

Since \(6^2 = 36\) and \(11^2 = 121\), we simplify the expression:

$$ \frac{\sqrt{36}}{\sqrt{121}} = \frac{6}{11} $$

Evaluate the square root of the fraction in part c

Similarly, we take the square root of the numerator and the denominator separately.

$$ \sqrt{\frac{1}{16}} = \frac{\sqrt{1}}{\sqrt{16}} $$

Since \(1^2 = 1\) and \(4^2 = 16\), we simplify the expression:

$$ \frac{\sqrt{1}}{\sqrt{16}} = \frac{1}{4} $$

Answer:

a) \(0.1\) (or \(\frac{1}{10}\))

b) \(\frac{6}{11}\)

c) \(\frac{1}{4}\) (or \(0.25\))