    Question

# Compare the given numbers by comparing their approximate values: 2√3,√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 2√3>√10As 2√3 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 2√3, 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<1.8⇒3.4<2√3<3.6∴2√3=3.4...–––– Similarly, the approximate value of √10 is 3.1...–––– Clearly, 3.4...––––>3.1...–––– ∴2√3>√10 Alternatively, the given surds can be squared and compared. (2√3)2=12(√10)2=10 ∵12>10⇒(2√3)2>(√10)2 If a & b are positive numbers and a2>b2⇒a>b ∴2√3>√10  Suggest Corrections  0      Similar questions  Explore more