Question

A decimal number is multiplied by itself. If the product is 7.29, find the number.

Answer 1

Answer:

2.7

Step-by-step explanation:

Since the decimal number is multiplied by itself; to find the original number, we need to find the square root of 7.29

7.29 can be written as 729/100 and upon prime factorising the numberator we get 7.29 = (3×3×3×3×3×3)/100 = 3⁶/100

Therefore on finding square root we get 3³/10 = 27/10 = 2.7

Hence 2.7 is the required answer

Answer 2

SOLUTION

GIVEN

A decimal number is multiplied by itself the product is 7.29

TO DETERMINE

The number

EVALUATION

Let the required number = n

So by the given condition

$\displaystyle \sf{ n \times n = 7.29}$

$\displaystyle \sf{ \implies \: {n}^{2} = 7.29}$

$\displaystyle \sf{ \implies \: n = \sqrt{7.29} }$

$\displaystyle \sf{ \implies \: n = \sqrt{ \frac{729}{100} } }$

$\displaystyle \sf{ \implies \: n = \sqrt{ \frac{3 \times 3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 5 \times 5} } }$

$\displaystyle \sf{ \implies \: n = \sqrt{ \frac{ {3}^{2} \times {3}^{2} \times {3}^{2} }{ {2}^{2} \times {5}^{2} } } }$

$\displaystyle \sf{ \implies \: n = \frac{3 \times 3 \times 3}{2 \times 5} }$

$\displaystyle \sf{ \implies \: n = \frac{27}{10} }$

$\displaystyle \sf{ \implies \: n = 2.7 }$

Hence the required decimal number = 2.7

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