Answer :
Answer:
30
Step-by-step explanation:
Using the properties of radicals
• [tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
• [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
given
2[tex]\sqrt{5}[/tex] × [tex]\sqrt{45}[/tex]
simplifying [tex]\sqrt{45}[/tex]
Consider the factors of 45, one of which is a perfect square
that is 45 = 9 × 5 , then
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex]
Then
2[tex]\sqrt{5}[/tex] × [tex]\sqrt{45}[/tex]
= 2[tex]\sqrt{5}[/tex] × 3[tex]\sqrt{5}[/tex]
= 2 × 3 × [tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex]
= 6 × 5
= 30
Answer:
30
Step-by-step explanation:
Given expression:
[tex]2\sqrt{5}\times\sqrt{45}[/tex]
To simplify the given expression, begin by applying the product rule, which states that the product of two radicals is equal to the root of the product of the radicands (the expressions under the radicals):
[tex]\sqrt{a} \times \sqrt{n}=\sqrt{a\times n}[/tex]
Therefore:
[tex]2\sqrt{5 \times 45}\\\\\\2\sqrt{225}[/tex]
Recall that 225 is a perfect square, as it is the square of 15. Therefore, we can rewrite 225 as 15²:
[tex]2\sqrt{15^2}[/tex]
The square root of the square of any non-negative real number is equal to the real number itself, so [tex]\sqrt{15^2}=15[/tex]. Therefore:
[tex]2\times 15\\\\\\30[/tex]
So, [tex]2\sqrt{5}\times\sqrt{45}[/tex] simplified is:
[tex]\LARGE\boxed{\boxed{30}}[/tex]
