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Negative exponents under square root sign

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We have (5X10^-4)(3X10^-10) under a square root sign (and then further calculations to complete the formula).  We are getting the correct answer but with the decimal point way off.  What do I need to know about negative exponents under square root signs?

Guest Mar 8, 2017

#3
+92806
+10

(5X10^-4)(3X10^-10)

$$\sqrt{(5*10^{-4})(3*10^{-10}) }\\ =\sqrt{5*10^{-4}*3*10^{-10} }\\ =\sqrt{5*3*10^{-4}*10^{-10} }\\ =\sqrt{15*10^{-4+-10} }\\ =\sqrt{15*10^{-14} }\\ =\sqrt{15}*\sqrt{10^{-14} }\\ =\sqrt{15}*10^{(-14*\frac{1}{2}) }\\ =\sqrt{15}*10^{(-7) }\\ =\sqrt{15}*\frac{1}{10^{(+7) }}\\ =\frac{\sqrt{15}}{10^7}\\$$

sqrt(15)/10^7 = 0.0000003872983346

Melody  Mar 8, 2017
#1
+7348
+4

We have (5X10^-4)(3X10^-10) under a square root sign (and then further calculations to complete the formula).  We are getting the correct answer but with the decimal point way off.  What do I need to know about negative exponents under square root signs?

$$\sqrt{{(5\times10^{-4})}\times(3\times10^{-10})}$$

$$=\sqrt{0.0005\times 0.0000000003}$$

$$=\sqrt{0.000 000 000 00015}$$

$$=3.60555127546\times 10^{-7}$$

!

asinus  Mar 8, 2017
#2
+12565
+10

sqrt[(5 x 10^-4)(3x10^-10)]  = sqrt (15 x 10^-14)  = sqrt(15)  x 10^-7 =

0.0000003872983346 = 3.872983346e-7

ElectricPavlov  Mar 8, 2017
#3
+92806
+10

(5X10^-4)(3X10^-10)

$$\sqrt{(5*10^{-4})(3*10^{-10}) }\\ =\sqrt{5*10^{-4}*3*10^{-10} }\\ =\sqrt{5*3*10^{-4}*10^{-10} }\\ =\sqrt{15*10^{-4+-10} }\\ =\sqrt{15*10^{-14} }\\ =\sqrt{15}*\sqrt{10^{-14} }\\ =\sqrt{15}*10^{(-14*\frac{1}{2}) }\\ =\sqrt{15}*10^{(-7) }\\ =\sqrt{15}*\frac{1}{10^{(+7) }}\\ =\frac{\sqrt{15}}{10^7}\\$$

sqrt(15)/10^7 = 0.0000003872983346

Melody  Mar 8, 2017
#4
0

thanks for the detailed answers. but asinus's answer does not agree with the others. why not?

atdhvaannkcse!

Guest Mar 8, 2017
#5
+12565
+5

Typo..... Asinus   found the square root of   13 x 10^-14   instead of 15 x 10^-14

ElectricPavlov  Mar 8, 2017