Question

Select all the correct answers. Could feel more than one answer.

Which expressions are equivalent to the given expression. Square root of 252
A. 126^1/2
B. 7•square root of 6
C. 18•square roof of 7
D. 6•square root of 7
E. 252^1/2

Answer 1

Explanation:

so, first, let's see the factors of 252 :

252 / 2 = 126

126 / 2 = 63

63 / 2 no

63 / 3 = 21

21 / 3 = 7

so, 252 = 2×2×3×3×7 =

= 4×9×7 =

= 36×7 =

= 42×6 =

= 18×14

and others. but these are closest to the given answer options.

A. is wrong. 126^(1/2) is the same as sqrt(126). that is of course not the same as sqrt(252).

B. is wrong. to leave 6 in the square root, the remaining factor is 42. and sqrt(42) is not 7.

C. is wrong. to leave 7 in the square root, the remaining factor is 36. and sqrt(36) is not 18.

D. is correct. see C. sqrt(36) = 6. so, sqrt(252) = sqrt(36×7) = 6×sqrt(7).

E. is correct. 252^(1/2) is exactly the same as sqrt(252). an exponent of 1/n means the nth root.

Answer 2

D

E

Explanation:

Prime factorize 252.

252 = 2 * 2 * 3 * 3 * 7

`\sf √(252)=√(2*2*3*3*7)`

`\sf = 2*3√(7)\\\\=6√(7)`

D

`\sf \text{The exponent form of } \ √(252)=252^{(1)/(2)}`

E