Question

1. estimate the square root of each of the following. do not use a calculator (3 marks)

a) 4.05
b) 0.17
c) 80/99

Explanation:

Estimate the square root of 4.05

Using the Square Root of Decimals and Perfect Squares knowledge points:
We want to estimate \(\sqrt{4.05}\).
We identify the closest perfect squares to \(4.05\):

$$4.05 \approx 4$$

Since \(4\) is a perfect square:

$$\sqrt{4} = 2$$

Therefore, we can estimate:

$$\sqrt{4.05} \approx 2$$

Estimate the square root of 0.17

Using the Square Root of Decimals and Perfect Squares knowledge points:
We want to estimate \(\sqrt{0.17}\).
We look for a perfect square decimal close to \(0.17\).
Since \(0.4^2 = 0.16\), \(0.16\) is extremely close to \(0.17\):

$$0.17 \approx 0.16$$

Taking the square root:

$$\sqrt{0.17} \approx \sqrt{0.16} = 0.4$$

Estimate the square root of 80/99

Using the Square Root of Fractions and Perfect Squares knowledge points:
We want to estimate \(\sqrt{\frac{80}{99}}\).
We look for perfect squares close to the numerator and the denominator:

$$80 \approx 81 \quad (\text{since } 9^2 = 81)$$

$$99 \approx 100 \quad (\text{since } 10^2 = 100)$$

We rewrite the fraction using these close perfect squares:

$$\frac{80}{99} \approx \frac{81}{100}$$

Taking the square root:

$$\sqrt{\frac{80}{99}} \approx \sqrt{\frac{81}{100}} = \frac{9}{10} = 0.9$$

Answer:

Question a

\(\sqrt{4.05} \approx 2\)

Question b

\(\sqrt{0.17} \approx 0.4\)

Question c

\(\sqrt{\frac{80}{99}} \approx 0.9\) (or \(\frac{9}{10}\))