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How do you simplify #sqrt5(5 sqrt3 - 2 sqrt4)#?

Answer 1

Eva Adamson

# = 5 sqrt15 -2 sqrt20#

#color(blue)(sqrt5) * ( 5 sqrt3 - 2 sqrt4)#

# = color(blue)(sqrt5) * ( 5 sqrt3 ) + color(blue)(sqrt5) * ( - 2 sqrt4)#

# = 5 * sqrt5 * sqrt3 + color(green)( (-2) * sqrt5 * sqrt4#

# = 5 * sqrt15 + color(green)( (-2) * sqrt20#

# = 5 sqrt15 -2 sqrt20#

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Answer 2

Julia Adams

To simplify the expression sqrt5(5 sqrt3 - 2 sqrt4), we can start by simplifying the square root of 4, which is 2. Then, we can distribute the square root of 5 to both terms inside the parentheses. This gives us:

sqrt5(5 sqrt3 - 2 sqrt4) = 5 sqrt5 sqrt3 - 2 sqrt5 sqrt4

Next, we simplify the square root of 5 times the square root of 3, which gives us sqrt15. Similarly, the square root of 5 times the square root of 4 simplifies to 2 sqrt5. Therefore, the expression simplifies to:

5 sqrt5 sqrt3 - 2 sqrt5 sqrt4 = 5 sqrt15 - 2 (2 sqrt5)

Finally, we can simplify further by multiplying 2 with sqrt5, which gives us 2 sqrt5. Therefore, the final simplified expression is:

5 sqrt15 - 2 (2 sqrt5) = 5 sqrt15 - 4 sqrt5

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.