Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.
√9x²-30x+25

Question

Simplify. Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.
√9x²-30x+25

paxpolaris · Answer

$$\sqrt {\left( a-b \right)^2}= \left| a-b \right|$$

anonymous · Answer

Yes this how far I got but when I turned it in I got this back

anonymous · Answer

√9x²-30x+25
9x^2 - 30x + 25 = (3x-5)^2  ; correct
 Square root of that will be +/- (3x-5).  ; incorrect,

paxpolaris · Answer

$$\sqrt{9x²-30x+25}=\sqrt{\left( 3x \right)^2-2\cdot \left( 3x \right)\cdot5 + 5^2}=\sqrt{\left( 3x-5 \right)^2}$$

paxpolaris · Answer

the square root symbol only has non-negative roots. eg: $$when\ a^2= 25 \implies a= \pm 5$$ 
$$but\ when\ a=\sqrt{25}; \implies a=+5$$

paxpolaris · Answer

so, $$\huge\sqrt{\left( 3x-5 \right)^2}= \left| \left( 3x-5 \right) \right|$$

anonymous · Answer

so that is the finally answer

paxpolaris · Answer

yea, just with the abs. value sign

anonymous · Answer

ok thanks that really helped