Question

Simplify 3 square root of 10 end root plus 7 square root of 15 end root minus 6 square root of 10 end root minus 4 square root of 15

Answer 1

Start with

`3√(10)+7√(15)-6√(10)-4√(15)`

We can factor the square root of 10 between the 1st and 3rd term, and the square root of 15 between the remaining two:

`√(10)(3-6)+√(15)(7-4) = -3√(10)+3√(15)`

Now we can factor 3 from both terms:

`3(√(15)-√(10))`

You can also use the rule

`√(ab)=√(a)√(b)`

To observe that

`3(√(15)-√(10))=3(√(5)√(3)-√(5)√(2))`

So we can factor the square root of 5 as well:

`3√(5)(√(3)-√(2))`

And the expression is fully simplified.

Answer 2

The expression is simplified to give -3√10 + 3√15

Surds refer to mathematical expressions containing square roots (√) or other roots (∛, ∜, etc.) that cannot be simplified to rational numbers. In simpler terms, they involve square roots of numbers that aren't perfect squares.

These expressions cannot be simplified to whole numbers or fractions because their square roots are irrational numbers (non-repeating and non-terminating decimals) and are not perfect squares.

From the information given, we have that;

3√10 + 7√15 - 6√10 - 4√15

collect the like terms, we have;

3√10 - 6√10 + 7√15- 4√15

subtract or add the like terms, we have;

-3√10 + 3√15