How do you simplify #sqrt15 * sqrt45#?

Answer 1

#15sqrt(3)#

Given,

#sqrt(15)*sqrt(45)#
Break down each radical using square numbers. Since #sqrt(15)# cannot be simplified any further, it is left as is.
#=sqrt(15)*sqrt(9*5)#
Since #sqrt(9)=3#, you can simplify the second radical.
#=sqrt(15)*3sqrt(5)#

Multiply the second radical by the first radical now that it has been simplified.

#=3sqrt(15*5)#
#=3sqrt(75)#
Break down #sqrt(75)# using square numbers.
#=3sqrt(25*3)#
Since #sqrt(25)=5#, you can simplify the radical.
#=3*5sqrt(3)#
#=color(green)(|bar(ul(color(white)(a/a)color(black)(15sqrt(3))color(white)(a/a)|)))#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To simplify ( \sqrt{15} \times \sqrt{45} ), you can use the properties of square roots.

  1. Recognize that ( \sqrt{15} ) and ( \sqrt{45} ) can be expressed as ( \sqrt{15} = \sqrt{3 \times 5} ) and ( \sqrt{45} = \sqrt{3 \times 3 \times 5} ).
  2. Apply the property ( \sqrt{a} \times \sqrt{b} = \sqrt{ab} ).
  3. Substitute the expressions under the square roots: ( \sqrt{15} \times \sqrt{45} = \sqrt{(3 \times 5) \times (3 \times 3 \times 5)} ).
  4. Simplify inside the square root: ( \sqrt{(3 \times 5) \times (3 \times 3 \times 5)} = \sqrt{3^2 \times 5^2} ).
  5. Apply the property ( \sqrt{a^2} = a ): ( \sqrt{3^2 \times 5^2} = 3 \times 5 ).
  6. Calculate: ( 3 \times 5 = 15 ).

Therefore, ( \sqrt{15} \times \sqrt{45} = 15 ).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7