Question

What is the closest approximate value of √ 23?
a. 4
b. 4.5
c. 4.8
d. 5

Answer 1

Option (C) is the answer.

$\large\underline{\large\underline{\text{Explanation}}}$

To find the closest approximation, we first need to consider another number $10 \sqrt{23} = \sqrt{2300}$.

Let's approximate the number.

As we can find out,

$\boxed{ \begin{aligned} &\rightarrow 40^{2}=1600\\\\&\rightarrow 45^{2}=1125\\\\&\rightarrow 48^{2}=2304\\\\&\rightarrow 50^{2}=2500. \end{aligned} }$

Now, we can say that,

$\cdots \longrightarrow 47<10\sqrt{23} <48.$

Hence, we can say that,

$\cdots \longrightarrow 10\sqrt{23} \approx 48.$

And hence,

$\cdots \longrightarrow \sqrt{23} \approx 4.8.$

Option (C) is the answer.

Answer 2

What is the closest approximate value of √23?

a.4

b.4.5

c.4.8✓

d.5

Let approximate the number

To find,

40² = 1600

45² = 1125

48² = 2304

50² = 2500

52² = 2704

54² = 2704

56² = 3136

58² = 3364

60² = 3600

Now, we can say that

= 47<10√23<48

Hence, we can say that

= 10√23≈48

And hence

= √23 ≈ 4.8

Option (c) is correct.