The simplified form of [tex]\sqrt{108} - 2\sqrt{300}[/tex] is [tex]-14\sqrt{3}[/tex].
Prime factorization is a way of expressing a number as a product of its prime factors.
A factor of a number that, when multiplied by itself, gives the original number called square root.
According to the given question.
We have an expression [tex]\sqrt{108} -2\sqrt{300}[/tex]
Prime factorization of 108 = 2 × 2 × 3 × 3 ×3[tex]=\sqrt{2^{2}.3^{3} } -2\sqrt{2^{2}.3^{3} }[/tex] = [tex]2^{2} .3^{3}[/tex]
Prime factorization of 300 = 2 × 2 × 3 × 5 × 5 = [tex]2^{2} . (3).5^{2}[/tex]
Therefore, the given expression can be written as
[tex]\sqrt{108} -2\sqrt{300}[/tex]
[tex]=\sqrt{2^{2} .3^{3} } -2\sqrt{2^{2} (3).5^{2} }[/tex]
[tex]=(2)(3)\sqrt{3} -2(2)(5)\sqrt{3}[/tex]
[tex]=6\sqrt{3} -20\sqrt{3}[/tex]
[tex]=-14\sqrt{3}[/tex].
Hence, [tex]\sqrt{108} - 2\sqrt{300} = -14\sqrt{3}[/tex]
Find out more information about square root and prime factorization here:
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