I need help in the steps simplifying these radicals.
Simplify 5√3 - √98 + √48 + 6√2
5√3 -7 √2+ 4√3+ 6√2
9√3 - √2
=5√3 - √49*2 + √16*3 + 6√2
=5√3 -7 √2+ 4√3+ 6√2
= 9√3 - √2
To simplify radicals, you need to apply certain rules and properties of radicals. Let's simplify each term step by step:
Step 1: Simplify 5√3
5√3 cannot be simplified any further because 3 does not have any perfect square factors.
Step 2: Simplify -√98
To simplify -√98, you need to find the largest perfect square factor of 98 that can be taken out of the square root. In this case, the largest perfect square factor is 49 (7^2). Rewrite -√98 as -7√(98/49).
Step 3: Simplify √48
To simplify √48, you need to find the largest perfect square factor of 48 that can be taken out of the square root. In this case, the largest perfect square factor is 16 (4^2). Rewrite √48 as 4√(48/16).
Step 4: Simplify 6√2
6√2 cannot be simplified any further because 2 does not have any perfect square factors.
Now, let's put the simplified terms together:
5√3 - √98 + √48 + 6√2 = 5√3 - 7√(98/49) + 4√(48/16) + 6√2
Next, we'll simplify the fractions under the radicals:
5√3 - 7√(98/49) + 4√(48/16) + 6√2
= 5√3 - 7(2/7)√98 + 4(2/4)√48 + 6√2
= 5√3 - 2√98 + 2√48 + 6√2
Finally, combine like terms:
= 5√3 - 2√(7*14) + 2√(4*12) + 6√2
= 5√3 - 2√(7*2^2) + 2√(2^2*3) + 6√2
= 5√3 - 4√7 + 4√3 + 6√2
So, the simplified expression is 5√3 - 4√7 + 4√3 + 6√2.