Which is equivalent to √3/√8 when denominator is "rationalized"?

Mathematics

1 answer:

TEA [102]3 years ago

4 0

Step-by-step explanation:

$\dfrac{\sqrt3}{\sqrt8}=\dfrac{\sqrt3\cdot\sqrt2}{\sqrt8\cdot\sqrt2}=\dfrac{\sqrt{3\cdot2}}{\sqrt{8\cdot2}}=\dfrac{\sqrt6}{\sqrt{16}}=\dfrac{\sqrt6}{4}$

$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16$

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Please help me :) once again

grigory [225]

Answer:

About 11.31 cm

Step-by-step explanation:

If one of the legs of a right iscosceles triangle is 8, then the length of the other one must also be 8. Therefore, by the Pythagorean Theorem:

$h=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}\approx11.31$

Hope this helps!

7 0

2 years ago

Read 2 more answers

Apply division algorithm to find the quotient and remainder on dividing the polynomial 3 x^ + 4 x^ square + 6 x + 9 by x^ + 3x +

Ulleksa [173]

I suppose you mean

$\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}$

$3x^3=3x\cdot x^2$ , and if we multiply $x^2+3x+7$ by $3x$ we get $3x^3+9x^2+21x$ . Subtracting this from the numerator gives a remainder of $-5x^2-15x+9$ .

$-5x^2=-5\cdot x^2$ , and multiplying $x^2+3x+7$ by $-5$ gives $-5x^2-15x-35$ . Subtracting this from the previous remainder gives a new remainder of $44$ .