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3 years ago

Combine, and simplify the following radical expressions: √7-5/√7+√8

Mathematics

2 answers:

solmaris [256]3 years ago

7 0

$\frac{\sqrt{7}-5}{\sqrt{7}+\sqrt{8}}$

Rationalize.

$-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}$

This can be further simplified to the decimal:

-0.43006...

I hope this helps :)

Svetllana [295]3 years ago

4 0

$\dfrac{\sqrt{7} - 5}{\sqrt{7}+ \sqrt{7} }$

Rationalise the denominator:

$\dfrac{(\sqrt{7} - 5)(\sqrt{7} - \sqrt{8}) }{(\sqrt{7}+ \sqrt{8}) (\sqrt{7} - \sqrt{8}) }$

$= \dfrac{(\sqrt{7})^2 - 5\sqrt{7} + 5\sqrt{8}- \sqrt{7}\sqrt{8} }{7 - 8 }$

$= \dfrac{(7 - 5\sqrt{7} + 10\sqrt{2}- 2\sqrt{14}}{-1 }$

$= -7 + 5\sqrt{7} - 10\sqrt{2} + 2\sqrt{14}$

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If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.

maks197457 [2]

Answer:

x = 4.5

Step-by-step explanation:

there's definitely other ways to solve this, but I used a proportion.

$\frac{3.5}{x} = \frac{14}{18}$

Then you can make this equation:

14x = 3.5 * 18

I solved for it and got 4.5 .

5 0

3 years ago

What is the distance rounded to the nearest tenth between the points (2 -2) and (6 3)

kotegsom [21]

Answer:

The distance between the points is approximately 6.4

Step-by-step explanation:

The given coordinates of the points are;

(2, -2), and (6, 3)

The distance between two points, 'A', and 'B', on the coordinate plane given their coordinates, (x₁, y₁), and (x₂, y₂) can be found using following formula;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

Substituting the known 'x', and 'y', values for the coordinates of the points, we have;

$l_{(2, \, -2), \ (6, \, 3) } = \sqrt{\left (3-(-2) \right )^{2}+\left (6-2 \right )^{2}} = \sqrt{5^2 + 4^2} = \sqrt{41}$

Therefore, the distance between the points, (2, -2), and (6, 3) = √(41) ≈ 6.4.

4 0

2 years ago

Simplify the square root of 3 times the fifth root of 3.

bogdanovich [222]

Answer:

<h2><em>Three to the three fifths power.</em></h2>

Step-by-step explanation:

The given expression is

$\sqrt{3\sqrt[5]{3} }$

To simplify this expression, we have to use a specific power property which allow us to transform a root into a power with a fractional exponent, the property states:

$\sqrt[n]{x^{m}}=x^{\frac{m}{n}}$

Applying the property, we have:

$\sqrt{3\sqrt[5]{3}}=\sqrt{3(3)^{\frac{1}{5}}}=(3(3)^{\frac{1}{5}})^{\frac{1}{2}}$

Now, we multiply exponents:

$(3(3)^{\frac{1}{5}})^{\frac{1}{2}}\\3^{\frac{1}{2}}3^{\frac{1}{10}}$

Then, we sum exponents to get the simplest form:

$3^{\frac{1}{2}}3^{\frac{1}{10}}=3^{\frac{1}{2}+\frac{1}{10}} =3^{\frac{10+2}{20}}=3^{\frac{12}{20}} \\\therefore \sqrt{3\sqrt[5]{3}}=3^{\frac{3}{5} }$