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2 years ago

Rationalize (4+√5)/(√15-√8)

Mathematics

2 answers:

dalvyx [7]2 years ago

8 0

Answer:

$\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}$

Step-by-step explanation:

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }$

To rationalize the above fraction multiple both numerator and denominator by the conjugate of its denominator.

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }$

We can simplify √8 like this :

√8 = √4 × √2

√8 = 2√2

Let us rationalize the above fraction now.

$\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }\\ \\\\\frac{(4+\sqrt{ 5})}{(\sqrt{15}-\sqrt{8}) }*\frac{(\sqrt{15}+2\sqrt{2} ) }{(\sqrt{15} +\sqrt{8})}$

Solve the brackets and roots.

$\frac{4(\sqrt{15}+2\sqrt{2})+\sqrt{5} (\sqrt{15} +2\sqrt{2}) }{\sqrt{ 15} * \sqrt{15} - \sqrt{8} * \sqrt{8} } }\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}$

Simplify the roots.

√75 = √25 × √3

√75 = 5√3

$\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}$

melisa1 [442]2 years ago

5 0

Answer:

See attached picture

Step-by-step explanation:

We rarionalize by multiplying with the conjugate of the denominator

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If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height

Tju [1.3M]

Correct question :

If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height x, and side length x + 4. A rectangle with length of x + 3 and width of one-half x. (x + 4) + x + (x + 2) = one-half x + (x + 3) (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3) 2 (x) + 2 (x + 2) = 2 (one-half x) + 2 (x + 3) x + (x + 2) + (x + 4) = 2 (x + 3 and one-half)

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Step-by-step explanation:

Given the following :

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b = x + 2 ; a = x ; c = x + 4

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(1) = (2)

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Answer:

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Step-by-step explanation:

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3 years ago

Determine if the table shows a proportional relationship.

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Any pair of values in a table that depicts a proportionate relationship have the same value for the proportionality constant, k, where k = y/x.

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k = 12.25/36.75 = 0.33

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k = 25.7/77.1 = 0.33

It is proportionate because the ratios of y across x are all equal to 1/3, which implies that the value of k is identical for all values.

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1 year ago

Rationalize (4+√5)/(√15-√8)​

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