Question

7root3/root10+root3-2root5/root6+root5-3root2/root15+3 root2 simplyfy

Answer 1

❥︎❥︎ANSWER࿐

-9√30 + 30√5 + 30√3 + 90√2

We first simplify all of the denominators by multiplying top and bottom by the radical:

(7√3/√10)(√10/√10) + √3 - (2√5/√6)(√6/√6) + √5 - (3√2/√15)(√15/√15) + 3√2

= 7√30/10 + √3 - 2√30/6 + √5 - 3√30/15 + 3√2

Multiply everything by 30 to simplify the fractions:

(7√30/10)(30) + 30√3 - (2√30/6)(30) + 30√5 - (3√30/15)(30) + 30*3√2

=210√30/10 + 30√3 - 60√30/6 + 30√5 - 90√30/15 + 90√2

Dividing we get

7√30 + 30√3 - 10√30 + 30√5 - 6√30 + 90√2

Combining like radicals we have

-9√30 + 30√3 + 30√5 + 90√2.