Answer:
1) The simplified radical form is [tex]\sqrt{36x^2}=6x[/tex]
2) The simplified radical form is [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]
3) The simplified radical form is [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]
4) The simplified radical form is [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]
Step-by-step explanation:
1) Given expression is [tex]\sqrt{36x^2}[/tex]
To find the simplified radical form of the given expression :
[tex]\sqrt{36x^2}[/tex]
[tex]=\sqrt{36\times x^2}[/tex]
[tex]=\sqrt{36}\times \sqrt{x^2}[/tex]
[tex]=\sqrt{6\times 6}\times \sqrt{x\times x}[/tex]
[tex]=6\times x[/tex]
[tex]\sqrt{36x^2}=6x[/tex]
Therefore the simplified radical form is [tex]\sqrt{36x^2}=6x[/tex]
2)Given expression is [tex]\sqrt{72x^3}[/tex]
To find the simplified radical form of the given expression :
[tex]\sqrt{72x^3}[/tex]
[tex]=\sqrt{72\times x^3}[/tex]
[tex]=\sqrt{72}\times \sqrt{x^3}[/tex]
[tex]=\sqrt{9\times 8}\times \sqrt{x\times x\times x}[/tex]
[tex]=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}[/tex]
[tex]=3\times 2\sqrt{2}\times x\sqrt{x}[/tex]
[tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]
Therefore the simplified radical form is [tex]\sqrt{72x^3}=6x\sqrt{2x}[/tex]
3) Given expression is [tex]\sqrt{15x^8}[/tex]
To find the simplified radical form of the given expression :
[tex]\sqrt{15x^8}[/tex]
[tex]=\sqrt{15\times x^8}[/tex]
[tex]=\sqrt{15}\times \sqrt{x^8}[/tex]
[tex]=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}[/tex]
[tex]=\sqrt{15}\times x^4[/tex]
[tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]
Therefore the simplified radical form is [tex]\sqrt{15x^8}=\sqrt{15}x^4[/tex]
4) Given expression is [tex]\sqrt{36x^7}[/tex]
To find the simplified radical form of the given expression :
[tex]\sqrt{36x^7}[/tex]
[tex]=\sqrt{36\times x^7}[/tex]
[tex]=\sqrt{36}\times \sqrt{x^7}[/tex]
[tex]=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}[/tex]
[tex]=6\times x^3\sqrt{x}[/tex]
[tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]
Therefore the simplified radical form is [tex]\sqrt{36x^7}=6x^3\sqrt{x}[/tex]