See the explanation
Explanation:
In this exercise, we have the following expression:
[tex]\sqrt{1120y^3}[/tex]
Applying prime factorization to 1120, we have:
[tex]1120=2^5\cdot 5\cdot 7[/tex]
So our expression becomes:
[tex]\sqrt{2^5\cdot 5\cdot 7y^3} \\ \\ or: \\ \\ \sqrt{2^4\cdot 2\cdot 5\cdot 7y^2\cdot y} \\ \\ Simplifying: \\ \\ \sqrt{2^4\cdot y^2}\sqrt{2\cdot 5\cdot 7y} \\ \\ 2^2\cdot y\sqrt{70y} \\ \\ 4y\sqrt{70y}[/tex]
So our first equivalent expression is:
[tex]\boxed{4y\sqrt{70y}}[/tex]
A second equivalent expression would be in exponent form:
[tex]4y\sqrt{70y} \\ \\ \\ By \ property: \\ \\ \sqrt[n]{x^m}=x^{m/n} \\ \\ \\ So: \\ \\ 4y\sqrt{70}y^{1/2} \\ \\ 4yy^{1/2} \sqrt{70} \\ \\ \\ By \ property: \\ \\ a^{m}a^{n}=a^{m+n} \\ \\ \boxed{4\sqrt{70}y^{3/2}}[/tex]
A third equivalent expression would be:
[tex]4\sqrt{70}y^{3/2} \\ \\ In \ radical \ form: \\ \\ \boxed{4\sqrt{70y^3}}[/tex]
Learn more:
Simplify: https://brainly.com/question/10644722
#LearnWithBrainly
