LaurenAshley1201
help :) multiply expression
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LaurenAshley1201
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\[2\sqrt{6}\times \sqrt{10}\]
Calcmathlete
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Multiply them seperately...
\[2\sqrt6 \times \sqrt{10} \implies 2\sqrt{6 \times 10} \implies 2 \sqrt{2 \times 3 \times 2 \times 5} \implies~?\]
Calcmathlete
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Can you finish from there? Can you simplify the radical?
violy
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|dw:1344751807375:dw| here is an example. :)
waterineyes
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@merp it is better if you do it here by your own..
waterineyes
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@LaurenAshley1201
\[\implies 2 \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5} = ??\]
LaurenAshley1201
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2 sqrt 60? i dont think im doing it right
waterineyes
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You can solve further for \(\sqrt{60}\)..
LaurenAshley1201
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2 sqrt 15
waterineyes
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\[\sqrt{60} = \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5}\]
Can you go further..??
violy
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think of a perfect square number that can go into 60.
waterineyes
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Yes..
waterineyes
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There is one 2 outside too..
Calcmathlete
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We have broken 60 down into prime factors for you. Remember this?
\[\sqrt{x \times x} = x\]Use the same rule...
waterineyes
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\[2 \times 2 \sqrt{15} = ??\]
violy
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do you mean sqrt (4 * 15) ?
waterineyes
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No..
LaurenAshley1201
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i dont know how to go any furhter
waterineyes
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\(\sqrt{60}\) is how much ??
waterineyes
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you have solved it above..
waterineyes
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\[\sqrt{60} = \sqrt{\color{blue}{\underline{2 \times 2}} \times 3 \times 5} = ??\]
violy
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its like sqrt( 5 x 5) = sqrt (25) = 5.
waterineyes
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Where are you having problem @LaurenAshley1201
violy
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let me give you an example: \[\sqrt{45}=\sqrt{3*3*5}=\sqrt{9} * \sqrt{5} = 3\sqrt{5}\]
LaurenAshley1201
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sqrt of 60 is 2 sqrt 15
violy
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you got it right now! :)
waterineyes
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In square root you can pull out one from a pair like this:
\[\sqrt{4 \times 4 \times 5}\]
Here you can see there are two 4's.
SO you can take one 4 outside and there will remain no 4 in the square root brackets:
So it becomes;
\[\sqrt{\color{green}{\underline{ 4 \times 4} \times 5}} \implies 4 \sqrt{5}\]
Calcmathlete
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Ok. Do you understand this at the very least?
\[\sqrt{3 \times 3} = \sqrt{3^2} = \sqrt{9} = 3\color{red}{\huge??????}\]
LaurenAshley1201
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yes i do
Calcmathlete
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THat's basically what you're doing here, it's just that you can make sense of it without showing all of the steps because you know the end result which is why we know that\[\sqrt{60} = \sqrt{2 \times 2 \times 3 \times 5} = 2\sqrt{15}\]
waterineyes
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\[2 \sqrt{60} = 2 \times (2 \sqrt{15}) = ??\]
LaurenAshley1201
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@Calcmathlete would that be my final answer?
Calcmathlete
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Not quite...you forgot the 2 that was already out there...
\[2 \times 2\sqrt{15} = ?\]
violy
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not yet, example: \[3*(4\sqrt{5}) = 3*4\sqrt{5} = 12\sqrt{5}\]
LaurenAshley1201
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i figuired it out,with everyones help ! thanks everyone
Calcmathlete
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Glad to help :)
violy
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my pleasure :)