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Simplify √48x^10y^13 to the form a√b

Sagot :

Question:

Solution:

Consider the following expression:

[tex]\sqrt{48x^{10}y^{13}}[/tex]

Applying the properties of radicals, we get:

[tex]\sqrt{48}\sqrt{x^{10}}\text{ }\sqrt{y^{13}}[/tex]

now, this is equivalent to:

[tex]4\sqrt{3}\sqrt{x^{10}}\text{ }\sqrt{y^{13}}[/tex]

this is equivalent to:

[tex]4\sqrt{3}\text{ x}^5y^6\sqrt{y}[/tex]

this is equivalent to:

[tex]4\text{x}^5y^6\sqrt{3}\text{ }\sqrt{y}[/tex]

finally, applying the properties of radicals, we get:

[tex]4\text{x}^5y^6\sqrt{3y}\text{ }[/tex]

Answer: we can conclude that the correct answer is:

[tex]a=4x^5y^6[/tex]

and

[tex]b=3y[/tex]

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