Question

1. name the two whole numbers whose squares are closest to 22.5

a. 9,25 b. 4,5 c. 4,9 d. 16,25

1. which fraction has a square root between 3 and 4?

i) \\(\frac{52}{3}\\)
ii) \\(\frac{61}{3}\\)
iii) \\(\frac{37}{4}\\)
iv) \\(\frac{79}{4}\\)

a. iv b. ii c. iii d. i

questions i should practice:

Explanation:

Question 3

Step1: Find squares of whole numbers

Calculate squares of whole numbers around the value 22.5. Let's check \(4^2 = 16\), \(5^2 = 25\), \(3^2 = 9\), \(6^2 = 36\).

Step2: Compare distances from 22.5

Distance of 16 from 22.5: \(|22.5 - 16| = 6.5\). Distance of 25 from 22.5: \(|25 - 22.5| = 2.5\). Distance of 9 from 22.5: \(|22.5 - 9| = 13.5\). So 4 (\(4^2 = 16\)) and 5 (\(5^2 = 25\)) are the whole numbers whose squares are closest to 22.5.

Step1: Recall range of square roots

We know that if \(3 < \sqrt{x} < 4\), then squaring all parts (since squaring is increasing for positive numbers), we get \(9 < x < 16\).

Step2: Analyze each fraction

• i) \(\frac{52}{3}\approx17.33\) (greater than 16, so \(\sqrt{\frac{52}{3}}\approx4.16>4\))
• ii) \(\frac{61}{3}\approx20.33\) (greater than 16, \(\sqrt{\frac{61}{3}}\approx4.51>4\))
• iii) \(\frac{37}{4} = 9.25\) (between 9 and 16, so \(3<\sqrt{\frac{37}{4}}<4\) as \(\sqrt{9}=3\) and \(\sqrt{16}=4\))
• iv) \(\frac{79}{4}=19.75\) (greater than 16, \(\sqrt{\frac{79}{4}}\approx4.44>4\))

Answer:

b. 4, 5

Question 4