QuestionCalculate $\frac{\sqrt{4^{2} \times 9 \times 16} \cdot \sqrt{4 \times 9^{2} \times 16} \cdot \sqrt{4 \times 9 \times 16^{2}}}{\sqrt{4 \times 9 \times 16}}$ . Choose the correct answer: (a) 12824 (b) 13824 (c) 23724 (d) 15924 (e) None.

Studdy Solution

STEP 1

Assumptions1. We are given an expression involving square roots and multiplication. . We need to simplify the expression and find its value.

STEP 2

We start by simplifying each square root in the numerator. The square root of a product is the product of the square roots, so we can simplify each term inside the square root separately.
$\sqrt{4^{2} \times9 \times16} = \sqrt{4^{2}} \times \sqrt{9} \times \sqrt{16}$ $\sqrt{4 \times9^{2} \times16} = \sqrt{4} \times \sqrt{9^{2}} \times \sqrt{16}$ $\sqrt{4 \times9 \times16^{2}} = \sqrt{4} \times \sqrt{9} \times \sqrt{16^{2}}$

STEP 3

Now we calculate the square roots.
$\sqrt{^{2}} =, \sqrt{9} =3, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9^{2}} =9, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9} =3, \sqrt{16^{2}} =16$

STEP 4

Now we multiply the results from step3.
$4 \times3 \times4 =48$ $2 \times9 \times4 =72$ $2 \times3 \times16 =96$

STEP 5

Now we multiply the results from step4.
$48 \times72 \times96 =331776$

STEP 6

Now we simplify the square root in the denominator.
$\sqrt{4 \times9 \times16} = \sqrt{4} \times \sqrt{9} \times \sqrt{16}$

STEP 7

Now we calculate the square roots.
$\sqrt{4} =2, \sqrt{9} =3, \sqrt{16} =4$

STEP 8

Now we multiply the results from step7.
$2 \times3 \times4 =24$

STEP 9

Now we divide the result from step5 by the result from step8.
$\frac{331776}{24} =13824$ So, the value of the given expression is13824. Therefore, the correct answer is (b)13824.

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QuestionCalculate $\frac{\sqrt{4^{2} \times 9 \times 16} \cdot \sqrt{4 \times 9^{2} \times 16} \cdot \sqrt{4 \times 9 \times 16^{2}}}{\sqrt{4 \times 9 \times 16}}$ . Choose the correct answer: (a) 12824 (b) 13824 (c) 23724 (d) 15924 (e) None.

Studdy Solution

STEP 1

Assumptions1. We are given an expression involving square roots and multiplication. . We need to simplify the expression and find its value.

STEP 2

STEP 3

Now we calculate the square roots.
$\sqrt{^{2}} =, \sqrt{9} =3, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9^{2}} =9, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9} =3, \sqrt{16^{2}} =16$

STEP 4

Now we multiply the results from step3.
$4 \times3 \times4 =48$ $2 \times9 \times4 =72$ $2 \times3 \times16 =96$

STEP 5

Now we multiply the results from step4.
$48 \times72 \times96 =331776$

STEP 6

Now we simplify the square root in the denominator.
$\sqrt{4 \times9 \times16} = \sqrt{4} \times \sqrt{9} \times \sqrt{16}$

STEP 7

Now we calculate the square roots.
$\sqrt{4} =2, \sqrt{9} =3, \sqrt{16} =4$

STEP 8

Now we multiply the results from step7.
$2 \times3 \times4 =24$

STEP 9

Now we divide the result from step5 by the result from step8.
$\frac{331776}{24} =13824$ So, the value of the given expression is13824. Therefore, the correct answer is (b)13824.

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Studdy Solution

STEP 1

Assumptions1. We are given an expression involving square roots and multiplication. . We need to simplify the expression and find its value.

STEP 2

STEP 3

Now we calculate the square roots.2=,9=3,16=\sqrt{^{2}} =, \sqrt{9} =3, \sqrt{16} =2​=,9​=3,16​==2,92=9,16=\sqrt{} =2, \sqrt{9^{2}} =9, \sqrt{16} =​=2,92​=9,16​==2,9=3,162=16\sqrt{} =2, \sqrt{9} =3, \sqrt{16^{2}} =16​=2,9​=3,162​=16

STEP 4

Now we multiply the results from step3.4×3×4=484 \times3 \times4 =484×3×4=482×9×4=722 \times9 \times4 =722×9×4=722×3×16=962 \times3 \times16 =962×3×16=96

STEP 5

Now we multiply the results from step4.48×72×96=33177648 \times72 \times96 =33177648×72×96=331776

STEP 6

Now we simplify the square root in the denominator.4×9×16=4×9×16\sqrt{4 \times9 \times16} = \sqrt{4} \times \sqrt{9} \times \sqrt{16}4×9×16​=4​×9​×16​

STEP 7

Now we calculate the square roots.4=2,9=3,16=4\sqrt{4} =2, \sqrt{9} =3, \sqrt{16} =44​=2,9​=3,16​=4

STEP 8

Now we multiply the results from step7.2×3×4=242 \times3 \times4 =242×3×4=24

STEP 9

Now we divide the result from step5 by the result from step8.33177624=13824\frac{331776}{24} =1382424331776​=13824So, the value of the given expression is13824. Therefore, the correct answer is (b)13824.

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Now we calculate the square roots.
$\sqrt{^{2}} =, \sqrt{9} =3, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9^{2}} =9, \sqrt{16} =$ $\sqrt{} =2, \sqrt{9} =3, \sqrt{16^{2}} =16$

Now we multiply the results from step3.
$4 \times3 \times4 =48$ $2 \times9 \times4 =72$ $2 \times3 \times16 =96$

Now we multiply the results from step4.
$48 \times72 \times96 =331776$

Now we simplify the square root in the denominator.
$\sqrt{4 \times9 \times16} = \sqrt{4} \times \sqrt{9} \times \sqrt{16}$

Now we calculate the square roots.
$\sqrt{4} =2, \sqrt{9} =3, \sqrt{16} =4$

Now we multiply the results from step7.
$2 \times3 \times4 =24$

Now we divide the result from step5 by the result from step8.
$\frac{331776}{24} =13824$ So, the value of the given expression is13824. Therefore, the correct answer is (b)13824.