How To Add Fractions Under Radicals

- we want to simplify the given fractions where the numerator and denominator are square roots. for these examples, it'll be helpful to rewrite this as the square root of a single fraction. this is normally not the case

How To Add Fractions Under Radicals, because a simplified radical cannot contain a fraction, but in this case we'd have the square root 200x to the 9th divided by 2x to the 5th. and since this fraction simplifies nicely,

it is going to help us simplify the original expression. so 200 divided by 2 = 100, so we'd have the square root of 100. and then x to the 9th divided by x to the 5th would be x to the 4th. and now the radicand is a perfect square. to show this, we can rewrite this as the square root of 100 = 10 x 10, and then x to the 4th = x to the 2nd x x to the 2nd.

so because we have a square root, if we circle pairs of equal factors, this is a perfect square factor, this is a perfect square factor, and so is this. so this simplifies perfectly. square root of 10 x 10 is 10. the square root of x squared is x here, as well as here, so we have 10x to the 2nd. so looking at the next example, we'll do the same thing.

we'll start by writing this as the square root of 735x to the 11th divided by 5x to the 6th. well, 735 divided by 5 = 147. so we have the square root of 147, then x to the 11th divided by x to the 6th. we subtract our exponents, this will be x to the 5th. and now 147x to the 5th is not a perfect square, so now we'll break this down into its prime factors. so 147 = 3 x 49 and of course 49 = 7 x 7.

so we can rewrite this as the square root of 3 x 7 x 7. and for x to 5th, because we're looking for groups of two equal factors, we'll write x to the 5th as x to the 2nd x x to the 2nd x one more factor of x. and now we'll circle groups of two equal factors here, here, and here. so the circled part represents the perfect square factors, which will simplify.

and the factors not circled will not simplify. so we'll have one factor of 7, one factor of x here and here. and then we're left with the square root of 3 x 3 or 3x. so this simplifies to 7x squared x the square root of 3x. okay, i hope you found this helpful. â