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Question

Compare the given numbers by comparing their approximate values: 23,10

A
23<10
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B
23>10
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C
It cannot be determined as there is no common term.
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Solution

The correct option is B 23>10
As 23 and 10 do not have like terms, find the approximate value of both the numbers using the perfect square method.

Let's find the approximate values up to one decimal place.

For 23, first we need to find approximate value of 3.

The largest perfect square smaller than 300 is 172.
And, the smallest perfect square larger than 300 is 182.

172<300<182
(dividing by 100 throughout the inequality)
172100<3.00<182100
(taking square root throughout the inequality)
172102<3<182102
1.7<3<1.83.4<23<3.623=3.4...––

Similarly, the approximate value of 10 is 3.1...––

Clearly, 3.4...––>3.1...––

23>10

Alternatively, the given surds can be squared and compared.
(23)2=12(10)2=10
12>10(23)2>(10)2

If a & b are positive numbers and a2>b2a>b

23>10

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