Mathematics, 04.12.2021 23:50 newjersey4015

Solve Please
(⁴√2+⁴√8)²

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Answer from: pakabigail7116

Simplified = 4 + 3 $\sqrt{2}\\$ , Decimal = 8.2426...

Step-by-step explanation:

Answer from: tmrodriguez1

$\left( \sqrt[4]{2} + \sqrt[4]{8} \right)^2\\\\=\left(\sqrt[4]2\right)^2 + \left(\sqrt[4]8\right)^2 + 2 \sqrt[4]2 \cdot \sqrt[4]8\\\\\\= \left(2^{\tfrac 14} \right)^2 + \left(8^{\tfrac 14} \right)^2+2\sqrt[4]{16}\\\\\\= 2^{\tfrac 12} +8^{\tfrac 12} + 2 \cdot \left(16\right)^{\tfrac 14}\\\\=\sqrt 2 +\sqrt 8+2 \cdot \left(2^4\right)^{\tfrac 14}\\\\=\sqrt 2 + \sqrt{4\times 2}+2\cdot 2\\\\= \sqrt 2 + 2\sqrt 2+4\\\\=4+ 3\sqrt 2$

Answer from: Quest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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