Chapter 10.1, Problem 1PE

(a)

To determine

To fill: The correct blank provided in the statement, ‘if $b^2=a$, then ___ is a square root of ___’.

(b)

To determine

To fill: The correct blank provided in the statement, ‘given $a>0$, the symbol $\sqrt{a}$ denotes the positive or ____ square root of a’.

(c)

To determine

To fill: The correct blank provided in the statement, ‘b is an nth root of a if ___=___’.

(d)

To determine

To fill: The correct blank provided in the statement, ‘given the symbol $\sqrt[n]{a}$, the value n is called the ___ and a is called the ___’.

(e)

To determine

To fill: The correct blank provided in the statement, ‘the symbol $\sqrt[3]{a}$ denotes the ___ root of a’.

(f)

To determine

Whether the expression $\sqrt{-4}$ is/is not a real number. Whether the expression $-\sqrt{4}$ is/is not a real number.

(g)

To determine

Whether the expression $\sqrt[n]{a^n}=\left|a\right|$ is odd/even. Whether the expression $\sqrt[n]{a^n}=a$ is odd/even.

(h)

To determine

To fill: The correct blank provided in the statement, ‘given a right triangle with legs a and b and hypotenuse c, the ____ theorem is stated as $a^2+b^2=$ ___’.

(i)

To determine

To fill: The correct blank provided in the statement, ‘in interval notation, the domain of $f\left(x\right)=\sqrt{x}$ is ___, whereas the domain of $g\left(x\right)=\sqrt[3]{x}$ is ___ ’.

(j)

To determine

The values $x=-5,x=-4,x=-3,x=-2,x=-1,x=0$ are not in the domain of $h\left(x\right)=\sqrt{x+3}$.