Irratsionaalavaldiste tegurdamine

Kursus „Arvuhulgad. Avaldised. Võrrandid ja võrratused”

Irratsionaalavaldiste, nagu ka ratsionaalavaldiste lihtsustamisel tuleb algebraliste murdude taandamisel ja ühenimeliseks teisendamisel avaldisi tegurdada. Ka juuravaldiste tegurdamisel saame kasutada sulgude ette toomist ja korrutamise abivalemeid.

Näiteid.

$\sqrt[3]{a^{2} b} - \sqrt[3]{a}$ = $\sqrt[3]{a} \cdot \sqrt[3]{a b} - \sqrt[3]{a}$ = $\sqrt[3]{a} (\sqrt[3]{a b} - 1)$

$a - \sqrt{a}$ = ${(\sqrt{a})}^{2} - \sqrt{a}$ = $\sqrt{a} (\sqrt{a} - 1)$

$x - y$ = ${(\sqrt{x})}^{2} - {(\sqrt{y})}^{2}$ = $(\sqrt{x} - \sqrt{y}) (\sqrt{x} + \sqrt{y})$

$2 + \sqrt[3]{4}$ = ${(\sqrt[3]{2})}^{3} + {(\sqrt[3]{2})}^{2}$ = $\sqrt[3]{2^{2}} (\sqrt[3]{2} + 1)$ = $\sqrt[3]{4} (\sqrt[3]{2} + 1)$

Ülesanded

$\sqrt[5]{x^{2} y} - \sqrt[5]{x y^{2}}$ =

\sqrt[3]{m} - m

\sqrt{2 x} - 2 x

\sqrt[3]{x^{2}} + 4 \sqrt[3]{x}

\sqrt{x} - 5 x

\sqrt[3]{a b^{2}} + \sqrt[3]{a^{2} b}

a - b

m - 2

2 m - 4 y

\frac{2 \sqrt[3]{m^{2}} + 5 \sqrt[3]{m n^{2}}}{\sqrt[3]{m}}

\frac{3 a + \sqrt{a}}{3 \sqrt{a} + 1}

\frac{x - 2 \sqrt{x}}{\sqrt{x}}

\frac{\sqrt[3]{a^{2}} - 2 \sqrt[3]{a}}{\sqrt[3]{a^{2}}}

\frac{2 x - \sqrt{x}}{2 \sqrt{x} - 1}

\frac{2 \sqrt{m} + m}{\sqrt{m}}

\frac{x - y}{\sqrt{x} - \sqrt{y}}

\frac{\sqrt{m} + \sqrt{n}}{m - n}

\frac{\sqrt{a} + 1}{a - 1}

Irratsionaalavaldiste tegurdamine

Kursus „Arvuhulgad. Avaldised. Võrrandid ja võrratused”

More like this

Ülesanded

More like this

Opiq score

	Tasks
	Chapter is studied

Irratsionaal­avaldiste tegurdamine

Kursus „Arvuhulgad. Avaldised. Võrrandid ja võrratused”

More like this

Ülesanded

More like this

Add content

Files to be added

Report Mistake

Only report errors related to the functionality or content of Opiq. Please describe the error as precisely as possible.

If you agree to share additional info, add your contact data (e-mail, phone).

Check to help us fight spam

Opiq uses cookies

Irratsionaalavaldiste tegurdamine