3 years ago

Simplify the square root of: √32

Mathematics

2 answers:

mylen [45]3 years ago

6 0

The square root of 32 is 5.65685

Wittaler [7]3 years ago

4 0

Answer:

4 $\sqrt{2}$

Step-by-step explanation:

factor the square root of 32

to get a total of 32, you do 4 times 4, which is 16

16 times 2 =32

16 is a perfect square so it's outside of the square root symbol, but you can't find the square root of 2 without it being irrational.

So,

final answer: 4 $\sqrt{2}$

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If log2 5 = a, log2 3 = b and log2 7 = c, determine an expression for log2 (25/21) in terms of a, b, and c

Ilia_Sergeevich [38]

Answer:

$2a - b -c$

Step-by-step explanation: We know that:

$log_{2} 5 = a\\log_{2} 3 = b\\log_2 7 = c\\$

and we want:

$log_2 \frac{25}{21}$ .

We can form the numerator using just the first fact (since 5^2 is 25) and the denominator using the latter two (since 3*7 = 21).

$log_2 \frac{25}{21} = log_2 \frac{5^2}{3*7}.$

The logarithm of a division can be expanded by subtracting the numerator and denominator (while still keeping the log). The logarithm of a product can be expanded by adding the terms while keeping the log. If the logarithm is raised to a power, we can bring it down as a factor:

$log_2 \frac{5^2}{3*7} = log_2(5)^2 - log_2 (3*7) = 2 log_2(5) - (log_2 3 + log_2 7)$