help...
5sqrt(8) - 3sqrt(18) + sqrt(3)
To simplify the given expression, we can start by simplifying each square root term separately.
Let's simplify √8 first:
We can rewrite 8 as the product of a perfect square and another number: 8 = 4 * 2. Then, using the property of square roots, we can split the square root: √8 = √(4 * 2) = √4 * √2 = 2√2.
Next, let's simplify √18:
Similarly, we can rewrite 18 as 9 * 2. Then, splitting the square root: √18 = √(9 * 2) = √9 * √2 = 3√2.
Lastly, we have √3, which cannot be simplified further.
Now, we can substitute these simplified terms back into the original expression:
5√8 - 3√18 + √3
= 5(2√2) - 3(3√2) + √3
= 10√2 - 9√2 + √3
= (10 - 9)√2 + √3
= √2 + √3
Therefore, the simplified form of the expression 5√8 - 3√18 + √3 is √2 + √3.
5√8 - 3√18 + √3
in general to change √k to a mixed radical, look for factors of k which are perfect squares
e.g. 18 = (3)(6) or 2(9)
the choice of (3)(6) does not do us any good, since neither factor is a perfect square
so your problem can be written as
5√4 √2 - 3√9 √2 + √3
= 5(2)√2 - 3(3)√2 + √3
= 10√2 - 9√2 + √3
= √2 + √3