[tex] \sqrt{18 } - \sqrt{12} \: is \: written \: as \: \sqrt[3]{2} - \sqrt[2]{3} [/tex]
Can you tell me how? I am confused....
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[tex] \sqrt{18 } - \sqrt{12} \: is \: written \: as \: \sqrt[3]{2} - \sqrt[2]{3} [/tex]
Can you tell me how? I am confused....
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Step-by-step explanation:
18 on its own isn't a perfect square, so we must find factors of 18 that will give us a perfect square. We can use the multiplication and division properties of radicals to do that!
√18=√9•2
√18=√9√2
We have factored 18 into 9and 2, so we can simplify
√9
to get our final answer.
√9√2=3√2
The simplest form of √18 is 3√2.
12 is 4 times 3:
√12 = √(4 × 3)
Use the rule:
√(4 × 3) = √4 × √3
And the square root of 4 is 2:
√4 × √3 = 2√3
So √12 is simpler as 2√3
Since our equation was √18-√12 is ³√2 - ²√3
Question:-
[tex] \sf\sqrt{18 } - \sqrt{12} \: is \: written \: as \: \sqrt[3]{2} - \sqrt[2]{3} .[/tex]
Solution:-
[tex] \sf \sqrt{18} - \sf \sqrt{12} [/tex]
[tex] \sf \sqrt{18} = \sqrt{2 \times 3 \times 3} [/tex]
[tex] \sf\longmapsto \sqrt{18} = \sqrt{(3 \times 3) \times 2} [/tex]
[tex] \sf \longmapsto \sqrt{18} = 3 \sqrt{2} \: \: \: - - > (1)[/tex]
[3 × 3 comes out from square root and becomes 3].
and
[tex] \sf \sqrt{12} = \sqrt{2 \times 2 \times 3} [/tex]
[tex] \sf \longmapsto \sqrt{12} = \sqrt{(2 \times 2) \times 3} [/tex]
[tex] \sf \longmapsto \sqrt{12} = 2\sqrt{3} \: \: \: - - > (2)[/tex]
[tex] \sf \: Now, \: \sqrt{18} - \sqrt{12} = 3\sqrt{2} - 2 \sqrt{3} \\ \sf \: from \: equation \: (1) \: and \: (2)[/tex]
Answer:-
[tex] \sf \red{\sf \sqrt{18} - \sf \sqrt{12} } \sf \: = \blue{3 \sqrt{2} - 2 \sqrt{3} }.[/tex]
Hope you have satisfied. ⚘