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TEA [102]
3 years ago
9

What is the following product? 3 root 5 times root 2

Mathematics
2 answers:
svet-max [94.6K]3 years ago
5 0

Answer:

\sqrt[6]{200}

Step-by-step explanation:

First of all, you need to know that you cannot multiply those radicals without having a common index (the little number outside the radical that sits in the curve of the radical).  One is a 3 and the other, without being stated outright, is understood to be a 2.  BUT we can make them like.  The index of a radical is the denominator of the exponential equivalent.  

\sqrt[3]{5}=5^{\frac{1}{3}} and

\sqrt{2}=2^{\frac{1}{2}}

See how the indexes are now the denominators of the rational exponents.  We can make them like by finding the LCM of 3 and 2...which is 6:

5^{\frac{1}{3}}=5^{\frac{2}{6}} and

2^{\frac{1}{2}}= 2^{\frac{3}{6}}

Now that the indexes are like, we rewrite them as radicals again:

\sqrt[6]{5^2}*\sqrt[6]{2^3} which, simplified, is

\sqrt[6]{25}*\sqrt[6]{8}

Now we can find the product which is

\sqrt[6]{200}

Crazy boy [7]3 years ago
3 0

\bf \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt[3]{5}\cdot \sqrt{2}\implies \sqrt[3]{5^1}\cdot \sqrt[2]{2^1}\implies 5^{\frac{1}{3}}\cdot 2^{\frac{1}{2}}\implies 5^{\frac{2}{6}}\cdot 2^{\frac{3}{6}}\implies \sqrt[6]{5^2}\cdot \sqrt[6]{2^3} \\\\\\ \sqrt[6]{25}\cdot \sqrt[6]{8}\implies \sqrt[6]{25\cdot 8}\implies \sqrt[6]{200}

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Step-by-step explanation:

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2 years ago
the initial vertical velocity of a rocket shot straight up is 42 meters per second. How long does it take for the rocket to retu
Snowcat [4.5K]
It takes 4.3 seconds for the rocket to return to earth.

The equation is:
0=-9.8t^2+v_0t+h_0
where -9.8m/sec² is the acceleration due to gravity, v₀ is the initial velocity, and h₀ is the initial height.  We will go from the assumption that the rocket is launched from the ground, so h₀=0, and we are told that the initial velocity, v₀, is 42.  This gives us:

0=-9.8t^2+42t

We will use the quadratic formula to solve this.  The quadratic formula is:
x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Plugging in our information we have:
t=\frac{-42\pm \sqrt{42^2-4(-9.8)(0)}}{2(-9.8)}
\\
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\\
\\=\frac{-42\pm \sqrt{1764}}{-19.6}
\\
\\=\frac{-42\pm 42}{-19.6}=\frac{-42-42}{-19.6} \text{ or } \frac{-42+42}{-19.6}
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8 0
3 years ago
Can one fifth be simplified
Svetradugi [14.3K]
No, and never, cus there ain't any numbers that are greater than 1 that can go into both of them.
<span>so basically if the numerator is 1, you can't simplify it anymore. Is Impossible.</span><span />
3 0
3 years ago
SAT Scores 1510 1480 2100 1800 1300 1250 1400 1430 1390 1520 The SAT scores for a group of 10 students are shown. What is the me
Minchanka [31]

Answer:

1580.0

Step-by-step explanation:

- Add all numbers and divide them by 10 (the amount of numbers).

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3 0
3 years ago
The Width of a rectangular Park is 10 metres shorter than its length.if the area of the park is 236 square metre find its length
madam [21]

Answer:

let length be l

breadth=l-10m

area of rectangular park=236m²

Step-by-step explanation:

area of rectangular park=236m²

l×(l-10)=236

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l²-2.l.5+5²-236-5²=0

(l-5)²-236-25=0

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l=16.15+5=21.15

b=l-10=21.15-10=11.15

3 0
2 years ago
Read 2 more answers
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