(2sqrt{8}-3sqrt{3}+5sqrt{32})-(3sqrt{27}-6sqrt{24}) eching

$$( 2 \sqrt { 8 } - 3 \sqrt { 3 } + 5 \sqrt { 32 } ) - ( 3 \sqrt { 27 } - 6 \sqrt { 24 } )$$

Baholash

$$12\left(\sqrt{6}+2\sqrt{2}-\sqrt{3}\right)\approx 42,55039272$$

Yechim qadamlari

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$2\times 2\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$4\sqrt{2}-3\sqrt{3}+5\sqrt{32}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Faktor: 32=4^{2}\times 2. \sqrt{4^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$4\sqrt{2}-3\sqrt{3}+5\times 4\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

20 hosil qilish uchun 5 va 4 ni ko'paytirish.

$$4\sqrt{2}-3\sqrt{3}+20\sqrt{2}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

24\sqrt{2} ni olish uchun 4\sqrt{2} va 20\sqrt{2} ni birlashtirish.

$$24\sqrt{2}-3\sqrt{3}-\left(3\sqrt{27}-6\sqrt{24}\right)$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$24\sqrt{2}-3\sqrt{3}-\left(3\times 3\sqrt{3}-6\sqrt{24}\right)$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\sqrt{24}\right)$$

Faktor: 24=2^{2}\times 6. \sqrt{2^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-6\times 2\sqrt{6}\right)$$

-12 hosil qilish uchun -6 va 2 ni ko'paytirish.

$$24\sqrt{2}-3\sqrt{3}-\left(9\sqrt{3}-12\sqrt{6}\right)$$

9\sqrt{3}-12\sqrt{6} teskarisini topish uchun har birining teskarisini toping.

$$24\sqrt{2}-3\sqrt{3}-9\sqrt{3}-\left(-12\sqrt{6}\right)$$

-12\sqrt{3} ni olish uchun -3\sqrt{3} va -9\sqrt{3} ni birlashtirish.

$$24\sqrt{2}-12\sqrt{3}-\left(-12\sqrt{6}\right)$$

-12\sqrt{6} ning teskarisi 12\sqrt{6} ga teng.

$$24\sqrt{2}-12\sqrt{3}+12\sqrt{6}$$