We will begin by working through Part (a): Simplify √18
To simplify a square root such as the one above, we must factor out perfect square numbers (this means we must find a number that multiplies to 18 and gives a whole number when we square root it). Using our knowledge that √9 is a perfect square, we should factor out a 9 from 18, as modeled below:
√18 = √(9*2)
We can separate this square root into two square roots multiplied together, as shown below:
√(9*2) = √9 * √2
Now, we should simplify √9, which equals 3, because 3 * 3 = 9.
√9 * √2 = 3 * √2 = 3√2
Therefore, √18 = 3√2.
Now, we can move on to the next problem: √6 * √15.
To begin this problem, we can multiply the square roots together, which means multiplying the numbers under the radical.
√6 * √15 = √(6*15) = √90
To simplify this, we use the same process as above:
√90 = √(10 * 9) = √9 * √10 = 3√10
Note: We know that this fully simplified because we cannot factor out another perfect square number from the number under the radical (10).
Therefore, your two answers are 3√2 and 3√10.
Hope this helps!
Answer:
5. -5x - 1
6. -x - 4
Step-by-step explanation:
5.
Distribute (get rid of parentheses):
-5x - 1
6.
Distribute (get rid of parentheses):
-x - 4
Answer:
8.75
Step-by-step explanation:
2*2+2.25+2.5=4+4.75=8.75
*assuming the smudged fraction is 1/4
Answer:
Solutions are (6,3) and (-2,3).
Step-by-step explanation:
From the first equation given we can write:
substituting for 
in the second equation given we get
∴ y=3
Putting y=3 in the first equation we get
x-2 = ±4
Hence x=6 or x=-2.
