Simplify ( square root of 8a^3+ square root of 5b^7)÷( square root of 13a^3- square root of 17b^7)

Math
(8a3+5b7)÷(13a3-17b7)
Rewrite the division as a fraction.
8a3+5b713a3-17b7
Simplify the numerator.
Tap for more steps…
Rewrite 8a3 as (2a)2⋅(2a).
Tap for more steps…
Factor 4 out of 8.
4(2)a3+5b713a3-17b7
Rewrite 4 as 22.
22⋅2a3+5b713a3-17b7
Factor out a2.
22⋅2(a2a)+5b713a3-17b7
Move 2.
22a2⋅2a+5b713a3-17b7
Rewrite 22a2 as (2a)2.
(2a)2⋅2a+5b713a3-17b7
Add parentheses.
(2a)2⋅(2a)+5b713a3-17b7
(2a)2⋅(2a)+5b713a3-17b7
Pull terms out from under the radical.
2a2a+5b713a3-17b7
Rewrite 5b7 as (b3)2⋅(5b).
Tap for more steps…
Factor out b6.
2a2a+5(b6b)13a3-17b7
Rewrite b6 as (b3)2.
2a2a+5((b3)2b)13a3-17b7
Reorder 5 and (b3)2.
2a2a+(b3)2⋅5b13a3-17b7
Add parentheses.
2a2a+(b3)2⋅(5b)13a3-17b7
2a2a+(b3)2⋅(5b)13a3-17b7
Pull terms out from under the radical.
2a2a+b35b13a3-17b7
2a2a+b35b13a3-17b7
Simplify the denominator.
Tap for more steps…
Rewrite 13a3 as a2⋅(13a).
Tap for more steps…
Factor out a2.
2a2a+b35b13(a2a)-17b7
Reorder 13 and a2.
2a2a+b35ba2⋅13a-17b7
Add parentheses.
2a2a+b35ba2⋅(13a)-17b7
2a2a+b35ba2⋅(13a)-17b7
Pull terms out from under the radical.
2a2a+b35ba13a-17b7
Rewrite 17b7 as (b3)2⋅(17b).
Tap for more steps…
Factor out b6.
2a2a+b35ba13a-17(b6b)
Rewrite b6 as (b3)2.
2a2a+b35ba13a-17((b3)2b)
Reorder 17 and (b3)2.
2a2a+b35ba13a-(b3)2⋅17b
Add parentheses.
2a2a+b35ba13a-(b3)2⋅(17b)
2a2a+b35ba13a-(b3)2⋅(17b)
Pull terms out from under the radical.
2a2a+b35ba13a-b317b
2a2a+b35ba13a-b317b
Multiply 2a2a+b35ba13a-b317b by a13a+b317ba13a+b317b.
2a2a+b35ba13a-b317b⋅a13a+b317ba13a+b317b
Combine fractions.
Tap for more steps…
Multiply 2a2a+b35ba13a-b317b and a13a+b317ba13a+b317b.
(2a2a+b35b)(a13a+b317b)(a13a-b317b)(a13a+b317b)
Expand the denominator using the FOIL method.
(2a2a+b35b)(a13a+b317b)a213a2+a(b3221ab)-b3(a221ba)-b617b2
Simplify.
(2a2a+b35b)(a13a+b317b)13a3-17b7
(2a2a+b35b)(a13a+b317b)13a3-17b7
Expand (2a2a+b35b)(a13a+b317b) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
2a2a(a13a+b317b)+b35b(a13a+b317b)13a3-17b7
Apply the distributive property.
2a2a(a13a)+2a2a(b317b)+b35b(a13a+b317b)13a3-17b7
Apply the distributive property.
2a2a(a13a)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
2a2a(a13a)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Simplify each term.
Tap for more steps…
Multiply a by a by adding the exponents.
Tap for more steps…
Move a.
2(a⋅a)2a13a+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply a by a.
2a22a13a+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
2a22a13a+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply 2a22a13a.
Tap for more steps…
Combine using the product rule for radicals.
2a213a(2a)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply 2 by 13.
2a226a⋅a+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Raise a to the power of 1.
2a226(a1a)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Raise a to the power of 1.
2a226(a1a1)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Use the power rule aman=am+n to combine exponents.
2a226a1+1+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Add 1 and 1.
2a226a2+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
2a226a2+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Reorder 26 and a2.
2a2a2⋅26+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Pull terms out from under the radical.
2a2(a26)+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply a2 by a by adding the exponents.
Tap for more steps…
Move a.
2(a⋅a2)26+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply a by a2.
Tap for more steps…
Raise a to the power of 1.
2(a1a2)26+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Use the power rule aman=am+n to combine exponents.
2a1+226+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
2a1+226+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Add 1 and 2.
2a326+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
2a326+2a2a(b317b)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply 2a2a(b317b).
Tap for more steps…
Combine using the product rule for radicals.
2a326+2a(b32a(17b))+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply 17 by 2.
2a326+2a(b334ab)+b35b(a13a)+b35b(b317b)13a3-17b7
2a326+2a(b334ab)+b35b(a13a)+b35b(b317b)13a3-17b7
Multiply b35b(a13a).
Tap for more steps…
Combine using the product rule for radicals.
2a326+2ab334ab+b3(a5b(13a))+b35b(b317b)13a3-17b7
Multiply 13 by 5.
2a326+2ab334ab+b3(a65ba)+b35b(b317b)13a3-17b7
2a326+2ab334ab+b3(a65ba)+b35b(b317b)13a3-17b7
Multiply b3 by b3 by adding the exponents.
Tap for more steps…
Move b3.
2a326+2ab334ab+b3a65ba+b3b35b17b13a3-17b7
Use the power rule aman=am+n to combine exponents.
2a326+2ab334ab+b3a65ba+b3+35b17b13a3-17b7
Add 3 and 3.
2a326+2ab334ab+b3a65ba+b65b17b13a3-17b7
2a326+2ab334ab+b3a65ba+b65b17b13a3-17b7
Multiply b65b17b.
Tap for more steps…
Combine using the product rule for radicals.
2a326+2ab334ab+b3a65ba+b617b(5b)13a3-17b7
Multiply 5 by 17.
2a326+2ab334ab+b3a65ba+b685b⋅b13a3-17b7
Raise b to the power of 1.
2a326+2ab334ab+b3a65ba+b685(b1b)13a3-17b7
Raise b to the power of 1.
2a326+2ab334ab+b3a65ba+b685(b1b1)13a3-17b7
Use the power rule aman=am+n to combine exponents.
2a326+2ab334ab+b3a65ba+b685b1+113a3-17b7
Add 1 and 1.
2a326+2ab334ab+b3a65ba+b685b213a3-17b7
2a326+2ab334ab+b3a65ba+b685b213a3-17b7
Reorder 85 and b2.
2a326+2ab334ab+b3a65ba+b6b2⋅8513a3-17b7
Pull terms out from under the radical.
2a326+2ab334ab+b3a65ba+b6(b85)13a3-17b7
Rewrite using the commutative property of multiplication.
2a326+2ab334ab+b3a65ba+85b6b13a3-17b7
Multiply b6 by b by adding the exponents.
Tap for more steps…
Move b.
2a326+2ab334ab+b3a65ba+85(b⋅b6)13a3-17b7
Multiply b by b6.
Tap for more steps…
Raise b to the power of 1.
2a326+2ab334ab+b3a65ba+85(b1b6)13a3-17b7
Use the power rule aman=am+n to combine exponents.
2a326+2ab334ab+b3a65ba+85b1+613a3-17b7
2a326+2ab334ab+b3a65ba+85b1+613a3-17b7
Add 1 and 6.
2a326+2ab334ab+b3a65ba+85b713a3-17b7
2a326+2ab334ab+b3a65ba+85b713a3-17b7
2a326+2ab334ab+b3a65ba+85b713a3-17b7
Simplify ( square root of 8a^3+ square root of 5b^7)÷( square root of 13a^3- square root of 17b^7)

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top