The mean proportional of -3 and 4 -3 is 2 -3-

The correct option is A True Mean proportional b=√(ac) nbsp; Here, nbsp; a=√(3), c=4√(3) nbsp; b=√(ac) =√((√(3))×(4√(3))) =√(4×(√(3))(√(3))) =√(4)×√ ...

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Standard X

Mathematics

Insertion of GP's between Two Numbers

The mean prop...

Question

The mean proportional of $\sqrt{3} a n d 4 \sqrt{3} i s 2 \sqrt{3}$ .

True

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False

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Solution

The correct option is A
True

Mean proportional $b = \sqrt{a c}$

Here, $a = \sqrt{3}, c = 4 \sqrt{3}$

$b = \sqrt{a c} = \sqrt{(\sqrt{3}) \times (4 \sqrt{3})} = \sqrt{4 \times (\sqrt{3}) (\sqrt{3})} = \sqrt{4} \times \sqrt{(\sqrt{3})^{2}} = 2 \times \sqrt{3} = 2 \sqrt{3}$

Hence the mean proportional of $\sqrt{3} a n d 4 \sqrt{3} i s 2 \sqrt{3} .$ This is a true statement.

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The mean proportional of √3 and 4√3 is 2√3.

The correct option is A True Mean proportional b=√ac Here, a=√3, c=4√3 b=√ac=√(√3)×(4√3)=√4×(√3)(√3)=√4×√(√3)2=2×√3=2√3 Hence the mean proportional of √3 and 4√3 is 2√3. This is a true statement.

The mean proportional of $\sqrt{3} a n d 4 \sqrt{3} i s 2 \sqrt{3}$ .