Simplify: 1) sqrt(0.49) 2) sqrt(49/100) 3) sqrt(100/49)

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems, following your specified format:

1) Simplify $\sqrt{0.49}$

Convert the decimal to a fraction.
$\sqrt{0.49} = \sqrt{\frac{49}{100}}$
Apply the property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ .
$\sqrt{\frac{49}{100}} = \frac{\sqrt{49}}{\sqrt{100}}$
Calculate the square roots.
$\frac{\sqrt{49}}{\sqrt{100}} = \frac{7}{10}$
Convert the fraction back to a decimal.
$\frac{7}{10} = 0.7$
The simplified expression is $\boxed{0.7}$ .

2) Simplify $\frac{4x^2 - 8x}{4x}$
Factor out the common term from the numerator.
$\frac{4x^2 - 8x}{4x} = \frac{4x(x - 2)}{4x}$
Cancel out the common factor $4x$ from the numerator and denominator.
$\frac{4x(x - 2)}{4x} = x - 2$
The simplified expression is $\boxed{x - 2}$ .

3) Simplify $(2m - 5)(m + 4)$
Use the distributive property (FOIL method) to multiply the binomials.
$(2m - 5)(m + 4) = 2m(m) + 2m(4) - 5(m) - 5(4)$ $= 2m^2 + 8m - 5m - 20$
Combine the like terms.
$2m^2 + (8m - 5m) - 20 = 2m^2 + 3m - 20$
The simplified expression is $\boxed{2m^2 + 3m - 20}$ .

Simplify: 1) sqrt(0.49) 2) sqrt((49)/(100)) 3) sqrt((100)/(49))