Question

Would 6 root 14 be the answer to (the square root of 21) (the square root of 24)?

Answer 1

The simplest way to do this is to find the square root of 21 and 24

Answer 2

\(\bf \cfrac{\sqrt{21}}{\sqrt{24}}?\)

Answer 3

\(\bf \sqrt{21}\cdot {\sqrt{24}}?\)

Answer 4

@jdoe0001 the second one (the multiplying one)

Answer 5

Simplify the following:
\[\sqrt(24) \]Factor 24 under the radical sign.
\[\sqrt(24) = \sqrt(8×3) = \sqrt(2^3×3): \]
\[\sqrt(2^3 3) \]Simplify powers.
\[\sqrt(2^3 3) = \sqrt(2^3) \sqrt(3) = 2 \sqrt(2) \sqrt(3): \]
\[2 \sqrt(2) \sqrt(3) \]
For
\[a>=0, \sqrt(a) \sqrt(b) = \sqrt(a b). \]
Apply this to
\[\sqrt(2) \sqrt(3). \]
\[\sqrt(2) \sqrt(3) = \sqrt(2×3): \]
\[2 \sqrt(2×3) \]
Multiply 2 and 3 together.
\[2×3 = 6: \]
Answer:
\[ 2 \sqrt(6 ) \]

Answer 6

\(\bf \sqrt{21}\cdot \sqrt{24}\implies \sqrt{21\cdot 24}\implies \sqrt{502}
\\ \quad \\
{\color{brown}{ 502\to 2\cdot 2\cdot 2\cdot 3\cdot 3\cdot 7\to 2^2\cdot 2\cdot 3^3\cdot 7}}
\\ \quad \\
\sqrt{502}\implies \sqrt{2^2\cdot 2\cdot 3^3\cdot 7}\implies ?\)

Answer 7

So \[6\sqrt{14}\] would be the simplest answer right? Cus since there's 2 twos and 2 threes, you bring that out of the radicand and you would multiply 2 x 3 getting 6. Then, you would multiply the two other numbers that are still the radicands and getting 7 x 2 or 14, right? Therefore \[6\sqrt{14}\] would be the answer, correct?

Answer 8

yeap \(\bf \sqrt{502}\implies \sqrt{2^2\cdot 2\cdot 3^3\cdot 7}\implies 2\cdot 3\sqrt{2\cdot 7}\implies 6\sqrt{14}\)